Journal articles: 'Bootstrap sample size'

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Shao, Jun. "Bootstrap sample size in nonregular cases." Proceedings of the American Mathematical Society 122, no. 4 (1994): 1251. http://dx.doi.org/10.1090/s0002-9939-1994-1227529-8.

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Thiele, Christian, and Gerrit Hirschfeld. "Confidence intervals and sample size planning for optimal cutpoints." PLOS ONE 18, no. 1 (2023): e0279693. http://dx.doi.org/10.1371/journal.pone.0279693.

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Various methods are available to determine optimal cutpoints for diagnostic measures. Unfortunately, many authors fail to report the precision at which these optimal cutpoints are being estimated and use sample sizes that are not suitable to achieve an adequate precision. The aim of the present study is to evaluate methods to estimate the variance of cutpoint estimations based on published descriptive statistics (‘post-hoc’) and to discuss sample size planning for estimating cutpoints. We performed a simulation study using widely-used methods to optimize the Youden index (empirical, normal, and transformed normal method) and three methods to determine confidence intervals (the delta method, the parametric bootstrap, and the nonparametric bootstrap). We found that both the delta method and the parametric bootstrap are suitable for post-hoc calculation of confidence intervals, depending on the sample size, the distribution of marker values, and the correctness of model assumptions. On average, the parametric bootstrap in combination with normal-theory-based cutpoint estimation has the best coverage. The delta method performs very well for normally distributed data, except in small samples, and is computationally more efficient. Obviously, not every combination of distributions, cutpoint optimization methods, and optimized metrics can be simulated and a lot of the literature is concerned specifically with cutpoints and confidence intervals for the Youden index. This complicates sample size planning for studies that estimate optimal cutpoints. As a practical tool, we introduce a web-application that allows for running simulations of width and coverage of confidence intervals using the percentile bootstrap with various distributions and cutpoint optimization methods.

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Geluk, Jaap, and Haan de. "On bootstrap sample size in extreme value theory." Publications de l'Institut Mathematique 71, no. 85 (2002): 21–26. http://dx.doi.org/10.2298/pim0271021g.

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Li, Jialiang, Bee Choo Tai, and David J. Nott. "Confidence interval for the bootstrapP-value and sample size calculation of the bootstrap test." Journal of Nonparametric Statistics 21, no. 5 (2009): 649–61. http://dx.doi.org/10.1080/10485250902770035.

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Stamps, Arthur E. "Bootstrap Investigation of Respondent Sample Size for Environmental Preference." Perceptual and Motor Skills 75, no. 1 (1992): 220–22. http://dx.doi.org/10.2466/pms.1992.75.1.220.

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Although environmental researchers use many different sizes of respondent samples, few environmental studies provide statistical rationales for selecting those sizes. This article utilizes bootstrap analysis to calculate split-block correlations of preferences of randomly selected respondents to a variety of environmental stimuli. Two analytic methods were used, raw score ratings and comparative choice. Analysis showed split-block correlations of .90 and higher could be achieved with 25 to 30 respondents with rating protocols and 10 to 15 respondents with comparative-choice protocols.

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Wei, Bei, Stephen M. S. Lee, and Xiyuan Wu. "Stochastically optimal bootstrap sample size for shrinkage-type statistics." Statistics and Computing 26, no. 1-2 (2014): 249–62. http://dx.doi.org/10.1007/s11222-014-9493-x.

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Chung, Kam‐Hin, and Stephen M. S. Lee. "Optimal Bootstrap Sample Size in Construction of Percentile Confidence Bounds." Scandinavian Journal of Statistics 28, no. 1 (2001): 225–39. http://dx.doi.org/10.1111/1467-9469.00233.

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Acquah, Henry de-Graft. "A Comparison of Bootstrap and Monte Carlo Approaches to Testing for Symmetry in the Granger and Lee Error Correction Model." Information Management and Business Review 5, no. 5 (2013): 240–44. http://dx.doi.org/10.22610/imbr.v5i5.1048.

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In this paper, I investigate the power of the Granger and Lee model of asymmetry via bootstrap and Monte Carlo techniques. The simulation results indicate that sample size, level of asymmetry and the amount of noise in the data generating process are important determinants of the power of the test for asymmetry based on bootstrap and Monte Carlo techniques. Additionally, the simulation results suggest that both bootstrap and Monte Carlo methods are successful in rejecting the false null hypothesis of symmetric adjustment in large samples with small error size and strong levels of asymmetry. In large samples, with small error size and strong levels of asymmetry, the results suggest that asymmetry test based on Monte Carlo methods achieve greater power gains when compared with the test for asymmetry based on bootstrap. However, in small samples, with large error size and subtle levels of asymmetry, the results suggest that asymmetry test based on bootstrap is more powerful than those based on the Monte Carlo methods. I conclude that both bootstrap and Monte Carlo algorithms provide valuable tools for investigating the power of the test of asymmetry.

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Cao, Leilei, Lulu Cao, Lei Guo, Kui Liu, and Xin Ding. "Reliability estimation for drive axle of wheel loader under extreme small sample." Advances in Mechanical Engineering 11, no. 3 (2019): 168781401983684. http://dx.doi.org/10.1177/1687814019836849.

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It is difficult to have enough samples to implement the full-scale life test on the loader drive axle due to high cost. But the extreme small sample size can hardly meet the statistical requirements of the traditional reliability analysis methods. In this work, the method of combining virtual sample expanding with Bootstrap is proposed to evaluate the fatigue reliability of the loader drive axle with extreme small sample. First, the sample size is expanded by virtual augmentation method to meet the requirement of Bootstrap method. Then, a modified Bootstrap method is used to evaluate the fatigue reliability of the expanded sample. Finally, the feasibility and reliability of the method are verified by comparing the results with the semi-empirical estimation method. Moreover, from the practical perspective, the promising result from this study indicates that the proposed method is more efficient than the semi-empirical method. The proposed method provides a new way for the reliability evaluation of costly and complex structures.

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Shaukat, S. Shahid, Toqeer Ahmed Rao, and Moazzam A. Khan. "Impact of sample size on principal component analysis ordination of an environmental data set: effects on eigenstructure." Ekológia (Bratislava) 35, no. 2 (2016): 173–90. http://dx.doi.org/10.1515/eko-2016-0014.

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AbstractIn this study, we used bootstrap simulation of a real data set to investigate the impact of sample size (N = 20, 30, 40 and 50) on the eigenvalues and eigenvectors resulting from principal component analysis (PCA). For each sample size, 100 bootstrap samples were drawn from environmental data matrix pertaining to water quality variables (p = 22) of a small data set comprising of 55 samples (stations from where water samples were collected). Because in ecology and environmental sciences the data sets are invariably small owing to high cost of collection and analysis of samples, we restricted our study to relatively small sample sizes. We focused attention on comparison of first 6 eigenvectors and first 10 eigenvalues. Data sets were compared using agglomerative cluster analysis using Ward’s method that does not require any stringent distributional assumptions.

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Acquah, Henry De-Graft. "Using Bootstrap Method to Evaluate the Power of Tests for Non-Linearity in Asymmetric Price Relationship." Journal of Economics and Behavioral Studies 5, no. 4 (2013): 237–41. http://dx.doi.org/10.22610/jebs.v5i4.399.

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This paper introduces and applies the bootstrap method to compare the power of the test for asymmetry in the Granger and Lee (1989) and Von Cramon-Taubadel and Loy (1996) models. The results of the bootstrap simulations indicate that the power of the test for asymmetry depends on various conditions such as the bootstrap sample size, model complexity, difference in adjustment speeds and the amount of noise in the data generating process used in the application. The true model achieves greater power when compared with the complex model. With small bootstrap sample size or large noise, both models display low power in rejecting the (false) null hypothesis of symmetry.

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Shvydka, Svitlana, Serhiy Levchuk, and Yelizoveta Sarabeeva. "Determination of rational sample size in parasitological studies by bootstrap method." Vìsnik Zaporìzʹkogo nacìonalʹnogo unìversitetu. Bìologìčnì nauki 1 (2019): 62–69. http://dx.doi.org/10.26661/2410-0943-2019-1-07.

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Qumsiyeh, Maher. "Using the Bootstrap for Estimating the Sample Size in Statistical Experiments." Journal of Modern Applied Statistical Methods 12, no. 1 (2013): 45–53. http://dx.doi.org/10.22237/jmasm/1367381280.

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Charlemagne, Gbemavo Dossou Sèblodo Judes, Cachon Fresnel Boris, and Lokonon Bruno. "Sample Size Affect Ethnobotanical Index Values: Bootstrap as a Remedial Approach." Open Journal of Applied Sciences 12, no. 11 (2022): 1758–69. http://dx.doi.org/10.4236/ojapps.2022.1211121.

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Varga, László, and András Zempléni. "Generalised block bootstrap and its use in meteorology." Advances in Statistical Climatology, Meteorology and Oceanography 3, no. 1 (2017): 55–66. http://dx.doi.org/10.5194/ascmo-3-55-2017.

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Abstract. In an earlier paper, Rakonczai et al.(2014) emphasised the importance of investigating the effective sample size in case of autocorrelated data. The simulations were based on the block bootstrap methodology. However, the discreteness of the usual block size did not allow for exact calculations. In this paper we propose a new generalisation of the block bootstrap methodology, which allows for any positive real number as expected block size. We relate it to the existing optimisation procedures and apply it to a temperature data set. Our other focus is on statistical tests, where quite often the actual sample size plays an important role, even in the case of relatively large samples. This is especially the case for copulas. These are used for investigating the dependencies among data sets. As in quite a few real applications the time dependence cannot be neglected, we investigated the effect of this phenomenon on the used test statistic. The critical value can be computed by the proposed new block bootstrap simulation, where the block size is determined by fitting a VAR model to the observations. The results are illustrated for models of the used temperature data.

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Zhang, Jun, Hui Ding, Ming Li, and Guan Bing Ma. "Small Sample Reliability Analysis of Automatic Ultrasonic Testing of Austenitic Steel Defect." Advanced Materials Research 544 (June 2012): 72–76. http://dx.doi.org/10.4028/www.scientific.net/amr.544.72.

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Reliability analysis of the procedure of ultrasonic technique before inspection has been proved to be essential to ensure the equipment operation safety. The conventional evaluation methods are based on statistical models and a remarkable sample size is needed to get a accurate result. In this work, the Bootstrap model for small sample data is established based on the re-sampling technique. The probability of detection (POD) curves in different conditions are calculated based on the Bootstrap model, and used for quantitative analysis the influence of inspection parameter on stainless steel auto ultrasonic testing result. The calculated result based on bootstrap model is compared with which based on model assisted POD method. The results indicate that Bootstrap model is an efficient tool for the reliability analysis of inspection with small sample data, and insure the inspection result.

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Hu, Yi-Ming, Zhong-Min Liang, Bin-Quan Li, and Zhong-Bo Yu. "Uncertainty Assessment of Hydrological Frequency Analysis Using Bootstrap Method." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/724632.

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The hydrological frequency analysis (HFA) is the foundation for the hydraulic engineering design and water resources management. Hydrological extreme observations or samples are the basis for HFA; the representativeness of a sample series to the population distribution is extremely important for the estimation reliability of the hydrological design value or quantile. However, for most of hydrological extreme data obtained in practical application, the size of the samples is usually small, for example, in China about 40~50 years. Generally, samples with small size cannot completely display the statistical properties of the population distribution, thus leading to uncertainties in the estimation of hydrological design values. In this paper, a new method based on bootstrap is put forward to analyze the impact of sampling uncertainty on the design value. By bootstrap resampling technique, a large number of bootstrap samples are constructed from the original flood extreme observations; the corresponding design value or quantile is estimated for each bootstrap sample, so that the sampling distribution of design value is constructed; based on the sampling distribution, the uncertainty of quantile estimation can be quantified. Compared with the conventional approach, this method provides not only the point estimation of a design value but also quantitative evaluation on uncertainties of the estimation.

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Fitrianto, Anwar, and Punitha Linganathan. "Comparisons between Resampling Techniques in Linear Regression: A Simulation Study." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 3 (2022): 345–53. http://dx.doi.org/10.18860/ca.v7i3.14550.

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The classic methods used in estimating the parameters in linear regression need to fulfill some assumptions. If the assumptions are not fulfilled, the conclusion is questionable. Resampling is one of the ways to avoid such problems. The study aims to compare resampling techniques in linear regression. The original data used in the study is clean, without any influential observations, outliers and leverage points. The ordinary least square method was used as the primary method to estimate the parameters and then compared with resampling techniques. The variance, p-value, bias, and standard error are used as a scale to estimate the best method among random bootstrap, residual bootstrap and delete-one Jackknife. After all the analysis took place, it was found that random bootstrap did not perform well while residual and delete-one Jackknife works quite well. Random bootstrap, residual bootstrap, and Jackknife estimate better than ordinary least square. Is was found that residual bootstrap works well in estimating the parameter in the small sample. At the same time, it is suggested to use Jackknife when the sample size is big because Jackknife is more accessible to apply than residual bootstrap and Jackknife works well when the sample size is big.

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Acquah, Henry de-Graft. "A Bootstrap Approach to Evaluating the Power of the Houckâ€™s Test for Asymmetry." Journal of Social and Development Sciences 4, no. 2 (2013): 69–73. http://dx.doi.org/10.22610/jsds.v4i2.737.

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The power of the conventional Houckâ€™s model of asymmetry is examined via parametric bootstrap simulation. The results of the bootstrap simulations indicate that the Houckâ€™s model has low power in rejecting the null of symmetric adjustment. The power of the test depends on the bootstrap sample size, level of asymmetry and the amount of noise in the data generating process used in an application. With a small bootstrap sample and large noise level, the Houckâ€™s model display low power in rejecting the null hypothesis of symmetry.

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Park, Joon Y. "AN INVARIANCE PRINCIPLE FOR SIEVE BOOTSTRAP IN TIME SERIES." Econometric Theory 18, no. 2 (2002): 469–90. http://dx.doi.org/10.1017/s0266466602182090.

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This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form and holds almost surely for all sample realizations. Our development relies upon the strong approximation and the Beveridge–Nelson representation of linear processes. For illustrative purposes, we apply our results and show the asymptotic validity of the sieve bootstrap for Dickey–Fuller unit root tests for the model driven by a general linear process with independent and identically distributed innovations. We thus provide a theoretical justification on the use of the bootstrap Dickey–Fuller tests for general unit root models, in place of the testing procedures by Said and Dickey and by Phillips.

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Calhoun, Gray. "BLOCK BOOTSTRAP CONSISTENCY UNDER WEAK ASSUMPTIONS." Econometric Theory 34, no. 6 (2018): 1383–406. http://dx.doi.org/10.1017/s0266466617000500.

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This paper weakens the size and moment conditions needed for typical block bootstrap methods (i.e., the moving blocks, circular blocks, and stationary bootstraps) to be valid for the sample mean of Near-Epoch-Dependent (NED) functions of mixing processes; they are consistent under the weakest conditions that ensure the original NED process obeys a central limit theorem (CLT), established by De Jong (1997, Econometric Theory 13(3), 353–367). In doing so, this paper extends De Jong’s method of proof, a blocking argument, to hold with random and unequal block lengths. This paper also proves that bootstrapped partial sums satisfy a functional CLT (FCLT) under the same conditions.

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Sari, Bruno Giacomini, Alessandro Dal’Col Lúcio, Tiago Olivoto, Dionatan Ketzer Krysczun, André Luís Tischler, and Lucas Drebes. "Interference of sample size on multicollinearity diagnosis in path analysis." Pesquisa Agropecuária Brasileira 53, no. 6 (2018): 769–73. http://dx.doi.org/10.1590/s0100-204x2018000600014.

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Abstract: The objective of this work was to evaluate the interference of sample size on multicollinearity diagnosis in path analysis. From the analyses of productive traits of cherry tomato, two Pearson correlation matrices were obtained, one with severe multicollinearity and the other with weak multicollinearity. Sixty-six sample sizes were designed, and from the amplitude of the bootstrap confidence interval, it was observed that sample size interfered on multicollinearity diagnosis. When sample size was small, the imprecision of the diagnostic criteria estimates interfered with multicollinearity diagnosis in the matrix with weak multicollinearity.

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Amalnerkar, Eshan, Tae Hee Lee, and Woochul Lim. "Reliability analysis using bootstrap information criterion for small sample size response functions." Structural and Multidisciplinary Optimization 62, no. 6 (2020): 2901–13. http://dx.doi.org/10.1007/s00158-020-02724-y.

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Kashani, M., M. Arashi, and M. R. Rabiei. "Resampling in Fuzzy Regression via Jackknife-after-Bootstrap (JB)." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29, no. 04 (2021): 517–35. http://dx.doi.org/10.1142/s0218488521500227.

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In fuzzy regression modeling, when the sample size is small, resampling methods are appropriate and useful for improving model estimation. However, in the commonly used bootstrap method, the standard errors of estimates are also random because of randomness existing in samples. This paper investigates the use of Jackknife-after-Bootstrap (JB) in fuzzy regression modeling to address this problem and produce estimates with smaller mean prediction errors. Performance analysis is carried out through some numerical illustrations and some interactive graphs to illustrate the superiority of the JB method compared to the bootstrap. Moreover, it is demonstrated that using the JB method, we have a significant model, with some sense; however, this is not the case using the bootstrap method.

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Palm, Franz C., Stephan Smeekes, and Jean-Pierre Urbain. "A SIEVE BOOTSTRAP TEST FOR COINTEGRATION IN A CONDITIONAL ERROR CORRECTION MODEL." Econometric Theory 26, no. 3 (2009): 647–81. http://dx.doi.org/10.1017/s0266466609990053.

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In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid. We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic components included are insensitive to the true value of the trends in the model and retain correct size.

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Barakat, H. M., Magdy E. El-Adll, and M. E. Sobh. "Bootstrapping $ m $-generalized order statistics with variable rank." AIMS Mathematics 7, no. 8 (2022): 13704–32. http://dx.doi.org/10.3934/math.2022755.

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<abstract><p>In this paper, several bootstrap properties of $ m $-generalized order statistics ($ m $-GOSs) with variable rank (central and intermediate) are revealed. We study the inconsistency, weak consistency and strong consistency of bootstrapping central and intermediate $ m $-GOSs when the normalizing constants are assumed to be known or estimated from the re-sampled data using a proper re-sample size. Furthermore, sufficient conditions for the weak and strong consistencies of the bootstrapping distributions of central and intermediate $ m $-GOSs based on the normalizing constant estimators are given. Finally, a simulation study is conducted to determine the optimal bootstrap re-sample size corresponding to the best fitting of the bootstrapping distribution.</p></abstract>

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K., Imasuen, and Orheruata U. M. "Estimating the Reliability Index Using Confidence Interval: A Comperism of the Fisher Z and the Bootstrap Confidence Interval Method." African Journal of Mathematics and Statistics Studies 5, no. 1 (2022): 55–66. http://dx.doi.org/10.52589/ajmss-zmragi1j.

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The study focused on estimating the reliability index using confidence interval by comparing the Fishers Z and the bootstrap confidence interval methods. The rational for the study was to examine the bootstrap and the Fisher –Z methods and finding out the better of the two. The population of the study consists of the senior secondary school students in Egor local government area, Edo State. There are a total of 12 school with 8,207 students. A sample size of 410 representing 5% of the total population of students were randomly selected from the 12 schools. The instrument for data collection was the Open Hemisphere Brain Dominance Scale 1.0 (OHBDS) a personality scale designed by Eric Jorgenson (2015). It was adapted for the study. The instrument was validated. The reliability was part of the issues raised in the study. The data were analyzed using the Pearson Product-Moment Correlation Coefficient to determine the reliability. The Fishers Z 95% and the Bootstrap (percentile and bias corrected and accelerated) confidence interval were also used. The findings revealed that as the sample size became large, the length of the interval became narrower; the three methods utilized in this study yielded the same length of the interval (width) when the same size was 100 and 150; and as the sample size increases, the bias corrected and accelerated bootstrap gave a shorter interval length, thereby becoming the best of the three method considered in the study. It was therefore recommended that reporting reliability should be based on interval estimation as against the point estimate, the sample size should be at least 100 and the bootstrap confidence interval should be adopted as it is not liable to the normality condition associated with the classical statistics.

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Acquah, Henry. "A bootstrap approach to evaluating the performance of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in selection of an asymmetric price relationship." Journal of Agricultural Sciences, Belgrade 57, no. 2 (2012): 99–110. http://dx.doi.org/10.2298/jas1202099d.

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This study addresses the problem of model selection in asymmetric price transmission models by combining the use of bootstrap methods with information theoretic selection criteria. Subsequently, parametric bootstrap technique is used to select the best model according to Akaike?s Information Criteria (AIC) and Bayesian Information Criteria (BIC). Bootstrap simulation results indicated that the performances of AIC and BIC are affected by the size of the data, the level of asymmetry and the amount of noise in the model used in the application. This study further establishes that the BIC is consistent and outperforms AIC in selecting the correct asymmetric price relationship when the bootstrap sample size is large.

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You, Jung S., and Minsoo Jeong. "A Performance Comparison of Various Bootstrap Methods for Diffusion Processes." Journal of Economics and Behavioral Studies 13, no. 4(J) (2021): 1–7. http://dx.doi.org/10.22610/jebs.v13i4(j).3185.

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In this paper, we compare the finite sample performances of various bootstrap methods for diffusion processes. Though diffusion processes are widely used to analyze stocks, bonds, and many other financial derivatives, they are known to heavily suffer from size distortions of hypothesis tests. While there are many bootstrap methods applicable to diffusion models to reduce such size distortions, their finite sample performances are yet to be investigated. We perform a Monte Carlo simulation comparing the finite sample properties, and our results show that the strong Taylor approximation method produces the best performance, followed by the Hermite expansion method.

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Byers, Jason S., and Jeff Gill. "Applied Geospatial Bayesian Modeling in the Big Data Era: Challenges and Solutions." Mathematics 10, no. 21 (2022): 4116. http://dx.doi.org/10.3390/math10214116.

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Two important trends in applied statistics are an increased usage of geospatial models and an increased usage of big data. Naturally, there has been overlap as analysts utilize the techniques associated with each. With geospatial methods such as kriging, the computation required becomes intensive quickly, even with datasets that would not be considered huge in other contexts. In this work we describe a solution to the computational problem of estimating Bayesian kriging models with big data, Bootstrap Random Spatial Sampling (BRSS), and first provide an analytical argument that BRSS produces consistent estimates from the Bayesian spatial model. Second, with a medium-sized dataset on fracking in West Virginia, we show that bootstrap sample effects from a full-information Bayesian model are reduced with more bootstrap samples and more observations per sample as in standard bootstrapping. Third, we offer a realistic illustration of the method by analyzing campaign donors in California with a large geocoded dataset. With this solution, scholars will not be constrained in their ability to apply theoretically relevant geospatial Bayesian models when the size of the data produces computational intractability.

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Radovanov, Boris, and Aleksandra Marcikić. "Testing The Performance Of The Investment Portfolio Using Block Bootstrap Method." Economic Themes 52, no. 2 (2014): 166–83. http://dx.doi.org/10.1515/ethemes-2014-0012.

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Abstract The aim of this paper is to create a stable model of investment portfolio optimization through a high degree of diversification and reduction of sudden changes in the allocation with monitoring of the dynamics of the impact factor. In this sense, there is bootstrap application procedure, which, without an excessive number of constraints involved in the optimization process provides solutions based on uncertain information. Thus defined, the optimization method has been patented by Michaud (1999) entitled re-sampled efficiency. Accordingly, this paper offers a comparison of the performance block bootstrap optimization models and traditional Markowitz's model inside and outside of the sample by applying the most frequently traded stocks on the BSE. The results show a better performance out of the sample and the presence of a larger number of shares forming the portfolio through bootstrap methodology. However, only through the traditional optimization process could be attained optimum according to the required limits. Such effects can be observed by comparing the limits of efficiency obtained through these optimization models. However, optimization-based methods bootstrap finds its place in reducing errors of assessment resulting from the limited sample size.

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Hwang, Inok, and Hyuncheol Kang. "Comparative Study on Testing Methods of Path Coefficient in Structural Equation Model." Korean Data Analysis Society 24, no. 3 (2022): 1007–16. http://dx.doi.org/10.37727/jkdas.2022.24.3.1007.

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When performing data analysis using the structural equation model, one of the main concerns is the estimation and testing of path coefficients. As a test method for path coefficients, a method using t-value, a method using a scaling test statistic of Satorra-Bentler, and a bootstrap method of Bollen-Stine are used. All of these methods are approximate testing methods, and in some cases provide different test results depending on the type of data and model given. In this paper, the type I error was calculated under special circumstances by using bootstrap simulation for the main test methods, and through this, the performance of these testing methods was evaluated. In terms of estimation and testing, the ML method was found to have a robust property in deviating from the normal distribution. On the other hand, in the case of the WLS method, the non-convergence rate was relatively high when the sample size was small, and the type I error was also relatively large. Therefore, it can be seen that the WLS method is useful when the sample size is quite large. In the case of the bootstrap methods, it can be seen that the type I error tends to increase as the sample size increases. Therefore, it is considered that a supplement to improve this phenomenon is necessary when applying the bootstrap methods.

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Li, Dongmei, and Timothy D. Dye. "Power and Stability Properties of Resampling-Based Multiple Testing Procedures with Applications to Gene Oncology Studies." Computational and Mathematical Methods in Medicine 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/610297.

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Resampling-based multiple testing procedures are widely used in genomic studies to identify differentially expressed genes and to conduct genome-wide association studies. However, the power and stability properties of these popular resampling-based multiple testing procedures have not been extensively evaluated. Our study focuses on investigating the power and stability of seven resampling-based multiple testing procedures frequently used in high-throughput data analysis for small sample size data through simulations and gene oncology examples. The bootstrap single-step minPprocedure and the bootstrap step-down minPprocedure perform the best among all tested procedures, when sample size is as small as 3 in each group and either familywise error rate or false discovery rate control is desired. When sample size increases to 12 and false discovery rate control is desired, the permutation maxTprocedure and the permutation minPprocedure perform best. Our results provide guidance for high-throughput data analysis when sample size is small.

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MANZATO, A. J., W. J. TADEI, and J. A. CORDEIRO. "Estimation of population profiles of two strains of the fly Megaselia scalaris (Diptera: Phoridae) by bootstrap simulation." Revista Brasileira de Biologia 60, no. 3 (2000): 415–24. http://dx.doi.org/10.1590/s0034-71082000000300006.

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Based on experimental population profiles of strains of the fly Megaselia scalaris (Phoridae), the minimal number of sample profiles was determined that should be repeated by bootstrap simulation process in order to obtain a confident estimation of the mean population profile and present estimations of the standard error as a precise measure of the simulations made. The original data are from experimental populations founded with SR and R4 strains, with three replicates, which were kept for 33 weeks by serial transfer technique in a constant temperature room (25 ± 1.0°C). The variable used was population size and the model adopted for each profile was a stationary stochastic process. By these simulations, the three experimental population profiles were enlarged so as to determine minimum sample size. After sample size was determined, bootstrap simulations were made in order to calculate confidence intervals and to compare the mean population profiles of these two strains. The results show that with a minimum sample size of 50, stabilization of means begins.

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Thomas, Hoben. "Effect Size Standard Errors for the Non-Normal Non-Identically Distributed Case." Journal of Educational Statistics 11, no. 4 (1986): 293–303. http://dx.doi.org/10.3102/10769986011004293.

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Suppose there are k independent studies and for each study the experimental and control groups have been sampled from independent but essentially arbitrary populations. The problem is to construct a plausible standard error of the effect size mean (effect sizes are standardized experimental-control group mean differences) when given only minimal sample statistic information. Standard errors based on the sample standard error, or bootstrap, will typically be much too large and have very large variance. A normal theory estimator may prove practically useful in more general settings. Asymptotic distribution-free estimators are provided for two cases.

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Dalposso, Gustavo H., Miguel A. Uribe-Opazo, and Jerry A. Johann. "Soybean yield modeling using bootstrap methods for small samples." Spanish Journal of Agricultural Research 14, no. 3 (2016): e0207. http://dx.doi.org/10.5424/sjar/2016143-8635.

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One of the problems that occur when working with regression models is regarding the sample size; once the statistical methods used in inferential analyzes are asymptotic if the sample is small the analysis may be compromised because the estimates will be biased. An alternative is to use the bootstrap methodology, which in its non-parametric version does not need to guess or know the probability distribution that generated the original sample. In this work we used a set of soybean yield data and physical and chemical soil properties formed with fewer samples to determine a multiple linear regression model. Bootstrap methods were used for variable selection, identification of influential points and for determination of confidence intervals of the model parameters. The results showed that the bootstrap methods enabled us to select the physical and chemical soil properties, which were significant in the construction of the soybean yield regression model, construct the confidence intervals of the parameters and identify the points that had great influence on the estimated parameters.

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Angelis, D. De, Peter Hall, and G. A. Young. "A note on coverage error of bootstrap confidence intervals for quantiles." Mathematical Proceedings of the Cambridge Philosophical Society 114, no. 3 (1993): 517–31. http://dx.doi.org/10.1017/s0305004100071802.

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AbstractAn interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size n−½, where n denotes sample size. By way of contrast, the error would be O(n−1) for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to o(n−½) by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error O(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-t are also analysed.

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Shvydka, S., V. Sarabeev, V. D. Estruch, and C. Cadarso-Suárez. "Optimum sample size to estimate mean parasite abundance in fish parasite surveys." Helminthologia 55, no. 1 (2018): 52–59. http://dx.doi.org/10.1515/helm-2017-0054.

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Summary To reach ethically and scientifically valid mean abundance values in parasitological and epidemiological studies this paper considers analytic and simulation approaches for sample size determination. The sample size estimation was carried out by applying mathematical formula with predetermined precision level and parameter of the negative binomial distribution estimated from the empirical data. A simulation approach to optimum sample size determination aimed at the estimation of true value of the mean abundance and its confidence interval (CI) was based on the Bag of Little Bootstraps (BLB). The abundance of two species of monogenean parasites Ligophorus cephali and L. mediterraneus from Mugil cephalus across the Azov-Black Seas localities were subjected to the analysis. The dispersion pattern of both helminth species could be characterized as a highly aggregated distribution with the variance being substantially larger than the mean abundance. The holistic approach applied here offers a wide range of appropriate methods in searching for the optimum sample size and the understanding about the expected precision level of the mean. Given the superior performance of the BLB relative to formulae with its few assumptions, the bootstrap procedure is the preferred method. Two important assessments were performed in the present study: i) based on CIs width a reasonable precision level for the mean abundance in parasitological surveys of Ligophorus spp. could be chosen between 0.8 and 0.5 with 1.6 and 1x mean of the CIs width, and ii) the sample size equal 80 or more host individuals allows accurate and precise estimation of mean abundance. Meanwhile for the host sample size in range between 25 and 40 individuals, the median estimates showed minimal bias but the sampling distribution skewed to the low values; a sample size of 10 host individuals yielded to unreliable estimates.

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Brown, Bryan W., and Roberto S. Mariano. "Predictors in Dynamic Nonlinear Models: Large-Sample Behavior." Econometric Theory 5, no. 3 (1989): 430–52. http://dx.doi.org/10.1017/s0266466600012603.

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The large-sample behavior of one-period-ahead and multiperiod-ahead predictors for a dynamic nonlinear simultaneous system is examined in this paper. Conditional on final values of the endogenous variables, the asymptotic moments of the deterministic, closed-form, Monte Carlo stochastic, and several variations of the residual-based stochastic predictor are analyzed. For one-period-ahead prediction, the results closely parallel our previous findings for static nonlinear systems. For multiperiod-ahead prediction similar results hold, except that the effective number of sample-period residuals available for use with the residual-based predictor is T/m, where T denotes sample size. In an attempt to avoid the problems associated with sample splitting, the complete enumeration predictor is proposed which is a multiperiod-ahead generalization of the one-period-ahead residual-based predictor. A bootstrap predictor is also introduced which is similar to the multiperiod-ahead Monte Carlo except disturbance proxies are drawn from the empirical distribution of the residuals. The bootstrap predictor is found to be asymptotically inefficient relative to both the complete enumeration and Monte Carlo predictors.

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Wang, Zuozhen. "Comparison of Sample Size by Bootstrap and by Formulas Based on Normal Distribution Assumption." Therapeutic Innovation & Regulatory Science 53, no. 2 (2019): 170–75. http://dx.doi.org/10.1177/2168479018778280.

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Lourdes Enginco Amarillo, Maria, A. L. Dans, and R. A. Delino. "Sample size estimates for estimating the true prevalence of a disease using bootstrap methods." Journal of Clinical Epidemiology 51 (February 1998): S28. http://dx.doi.org/10.1016/s0895-4356(98)90086-5.

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Chaibub Neto, Elias. "Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications." PLOS ONE 10, no. 6 (2015): e0131333. http://dx.doi.org/10.1371/journal.pone.0131333.

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Hounyo, Ulrich. "A LOCAL GAUSSIAN BOOTSTRAP METHOD FOR REALIZED VOLATILITY AND REALIZED BETA." Econometric Theory 35, no. 2 (2018): 360–416. http://dx.doi.org/10.1017/s0266466618000129.

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This article introduces a local Gaussian bootstrap method useful for the estimation of the asymptotic distribution of high-frequency data-based statistics such as functions of realized multivariate volatility measures as well as their asymptotic variances. The new approach consists of dividing the original data into nonoverlapping blocks ofMconsecutive returns sampled at frequencyh(whereh−1denotes the sample size) and then generating the bootstrap observations at each frequency within a block by drawing them randomly from a mean zero Gaussian distribution with a variance given by the realized variance computed over the corresponding block.Our main contributions are as follows. First, we show that the local Gaussian bootstrap is first-order consistent when used to estimate the distributions of realized volatility and realized betas under assumptions on the log-price process which follows a continuous Brownian semimartingale process. Second, we show that the local Gaussian bootstrap matches accurately the first four cumulants of realized volatility up too(h), implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009,Econometrica77(1), 283–306), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able to provide second-order refinements for the realized beta, which is also an improvement of the existing bootstrap results in Dovonon, Gonçalves, and Meddahi (2013,Journal of Econometrics172, 49–65) (where the pairs bootstrap was shown not to be second-order correct under general stochastic volatility). In addition, we highlight the connection between the local Gaussian bootstrap and the local Gaussianity approximation of continuous semimartingales established by Mykland and Zhang (2009,Econometrica77, 1403–1455) and show the suitability of this bootstrap method to deal with the new class of estimators introduced in that article. Lastly, we provide Monte Carlo simulations and use empirical data to compare the finite sample accuracy of our new bootstrap confidence intervals for integrated volatility with the existing results.

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Fan, Yanqin, and Sang Soo Park. "SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE." Econometric Theory 26, no. 3 (2009): 931–51. http://dx.doi.org/10.1017/s0266466609990168.

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In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-nbootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than-nbootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.

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Dziak, John J., Stephanie T. Lanza, and Xianming Tan. "Effect Size, Statistical Power, and Sample Size Requirements for the Bootstrap Likelihood Ratio Test in Latent Class Analysis." Structural Equation Modeling: A Multidisciplinary Journal 21, no. 4 (2014): 534–52. http://dx.doi.org/10.1080/10705511.2014.919819.

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Marill, Keith A., Yuchiao Chang, Kim F. Wong, and Ari B. Friedman. "Estimating negative likelihood ratio confidence when test sensitivity is 100%: A bootstrapping approach." Statistical Methods in Medical Research 26, no. 4 (2015): 1936–48. http://dx.doi.org/10.1177/0962280215592907.

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Objectives Assessing high-sensitivity tests for mortal illness is crucial in emergency and critical care medicine. Estimating the 95% confidence interval (CI) of the likelihood ratio (LR) can be challenging when sample sensitivity is 100%. We aimed to develop, compare, and automate a bootstrapping method to estimate the negative LR CI when sample sensitivity is 100%. Methods The lowest population sensitivity that is most likely to yield sample sensitivity 100% is located using the binomial distribution. Random binomial samples generated using this population sensitivity are then used in the LR bootstrap. A free R program, “bootLR,” automates the process. Extensive simulations were performed to determine how often the LR bootstrap and comparator method 95% CIs cover the true population negative LR value. Finally, the 95% CI was compared for theoretical sample sizes and sensitivities approaching and including 100% using: (1) a technique of individual extremes, (2) SAS software based on the technique of Gart and Nam, (3) the Score CI (as implemented in the StatXact, SAS, and R PropCI package), and (4) the bootstrapping technique. Results The bootstrapping approach demonstrates appropriate coverage of the nominal 95% CI over a spectrum of populations and sample sizes. Considering a study of sample size 200 with 100 patients with disease, and specificity 60%, the lowest population sensitivity with median sample sensitivity 100% is 99.31%. When all 100 patients with disease test positive, the negative LR 95% CIs are: individual extremes technique (0,0.073), StatXact (0,0.064), SAS Score method (0,0.057), R PropCI (0,0.062), and bootstrap (0,0.048). Similar trends were observed for other sample sizes. Conclusions When study samples demonstrate 100% sensitivity, available methods may yield inappropriately wide negative LR CIs. An alternative bootstrapping approach and accompanying free open-source R package were developed to yield realistic estimates easily. This methodology and implementation are applicable to other binomial proportions with homogeneous responses.

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de la Cruz, Rolando, Claudio Fuentes, Cristian Meza, and Vicente Núñez-Antón. "Error-rate estimation in discriminant analysis of non-linear longitudinal data: A comparison of resampling methods." Statistical Methods in Medical Research 27, no. 4 (2016): 1153–67. http://dx.doi.org/10.1177/0962280216656246.

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Consider longitudinal observations across different subjects such that the underlying distribution is determined by a non-linear mixed-effects model. In this context, we look at the misclassification error rate for allocating future subjects using cross-validation, bootstrap algorithms (parametric bootstrap, leave-one-out, .632 and [Formula: see text]), and bootstrap cross-validation (which combines the first two approaches), and conduct a numerical study to compare the performance of the different methods. The simulation and comparisons in this study are motivated by real observations from a pregnancy study in which one of the main objectives is to predict normal versus abnormal pregnancy outcomes based on information gathered at early stages. Since in this type of studies it is not uncommon to have insufficient data to simultaneously solve the classification problem and estimate the misclassification error rate, we put special attention to situations when only a small sample size is available. We discuss how the misclassification error rate estimates may be affected by the sample size in terms of variability and bias, and examine conditions under which the misclassification error rate estimates perform reasonably well.

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Verbyla, David. "Potential prediction bias in regression and discriminant analysis." Canadian Journal of Forest Research 16, no. 6 (1986): 1255–57. http://dx.doi.org/10.1139/x86-222.

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Prediction bias is the difference between a model's apparent and actual prediction errors. Prediction bias is likely to occur when a model contains many independent variables relative to sample size or when many different sets of independent variables are tested by a stepwise procedure. Examples of potential prediction bias are illustrated by comparing published models with models developed using random numbers. Model prediction bias can be estimated by using a resampling procedure called the bootstrap. The bootstrap procedure is illustrated with a simple example.

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Dias Duarte Machado, Luiz Gabriel, Lior Mevorach, Victor De Oliveira Corrêa, et al. "Study of hippocampal size and age." Italian Journal of Anatomy and Embryology 125, no. 1 (2022): 59–65. http://dx.doi.org/10.36253/ijae-11867.

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Objective (or background): The hippocampus is a thoroughly studied structure of the temporal lobe. In contrast to our current knowledge of hippocampal anatomy, neurophysiology and pathophysiology, scientific literature on the relationship between the hippocampal size and age is limited. Our study aims to further the understanding of this relationship. Methods: 16 hippocampi were anatomized, photographed, measured and analyzed in comparison to age and gender using Pearson and bootstrap analyses with IBM SPSS®. Results: The results for all three independent variables of size, age and gender were not statistically significant. Conclusions: We were unable to show a statistically significant result on the correlation between the size of the hippocampus and age due to small sample size.

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Austin, Peter C., and Ewout W. Steyerberg. "Events per variable (EPV) and the relative performance of different strategies for estimating the out-of-sample validity of logistic regression models." Statistical Methods in Medical Research 26, no. 2 (2014): 796–808. http://dx.doi.org/10.1177/0962280214558972.

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We conducted an extensive set of empirical analyses to examine the effect of the number of events per variable (EPV) on the relative performance of three different methods for assessing the predictive accuracy of a logistic regression model: apparent performance in the analysis sample, split-sample validation, and optimism correction using bootstrap methods. Using a single dataset of patients hospitalized with heart failure, we compared the estimates of discriminatory performance from these methods to those for a very large independent validation sample arising from the same population. As anticipated, the apparent performance was optimistically biased, with the degree of optimism diminishing as the number of events per variable increased. Differences between the bootstrap-corrected approach and the use of an independent validation sample were minimal once the number of events per variable was at least 20. Split-sample assessment resulted in too pessimistic and highly uncertain estimates of model performance. Apparent performance estimates had lower mean squared error compared to split-sample estimates, but the lowest mean squared error was obtained by bootstrap-corrected optimism estimates. For bias, variance, and mean squared error of the performance estimates, the penalty incurred by using split-sample validation was equivalent to reducing the sample size by a proportion equivalent to the proportion of the sample that was withheld for model validation. In conclusion, split-sample validation is inefficient and apparent performance is too optimistic for internal validation of regression-based prediction models. Modern validation methods, such as bootstrap-based optimism correction, are preferable. While these findings may be unsurprising to many statisticians, the results of the current study reinforce what should be considered good statistical practice in the development and validation of clinical prediction models.

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Journal articles on the topic 'Bootstrap sample size'

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