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Journal articles on the topic 'Profile likelihood confidence regions'

Author: Grafiati

Published: 10 January 2023

Last updated: 28 January 2023

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1

Pek, Jolynn, and Hao Wu. "Profile Likelihood-Based Confidence Intervals and Regions for Structural Equation Models." Psychometrika 80, no. 4 (April 30, 2015): 1123–45. http://dx.doi.org/10.1007/s11336-015-9461-1.

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2

Montoya, José A., Gudelia Figueroa-Preciado, and Mayra Rosalia Tocto-Erazo. "FLAT LIKELIHOODS: SIR-POISSON MODEL CASE." Revista de la Facultad de Ciencias 11, no. 2 (July 1, 2022): 74–99. http://dx.doi.org/10.15446/rev.fac.cienc.v11n2.100986.

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Systems of differential equations are used as the basis to define mathematical structures for moments, like the mean and variance, of random variables probability distributions. Nevertheless, the integration of a deterministic model and a probabilistic one, with the aim of describing a random phenomenon, and take advantage of the observed data for making inferences on certain population dynamic characteristics, can lead to parameter identifiability problems. Furthermore, approaches to deal with those problems are usually inappropriate. In this paper, the shape of the likelihood function of a SIR-Poisson model is used to describe the relationship between flat likelihoods and the identifiability parameter problem. In particular, we show how a flattened shape for the profile likelihood of the basic reproductive number R0, arises as the observed sample (over time) becomes smaller, causing ambiguity regarding the shape of the average model behavior. We conducted some simulation studies to analyze the flatness severity of the R0 likelihood, and the coverage frequency of the likelihood-confidence regions for the model parameters. Finally, we describe some approaches to deal the practical identifiability problem, showing the impact those can have on inferences. We believe this work can help to raise awareness on the way statistical inferences can be affected by a priori parameter assumptions and the underlying relationship between them, as well as by model reparameterizations and incorrect model assumptions.

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Zou, Yuye, and Chengxin Wu. "Statistical Inference for the Heteroscedastic Partially Linear Varying-Coefficient Errors-in-Variables Model with Missing Censoring Indicators." Discrete Dynamics in Nature and Society 2021 (June 7, 2021): 1–26. http://dx.doi.org/10.1155/2021/1141022.

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In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. Based on regression calibration, imputation, and inverse probability weighted methods, we define a class of modified profile least square estimators of the parameter and local linear estimators of the coefficient function, which are applied to constructing estimators of the error variance function. In order to improve the estimation accuracy and take into account the heteroscedastic error, reweighted estimators of the parameter and coefficient function are developed. At the same time, we apply the empirical likelihood method to construct confidence regions and maximum empirical likelihood estimators of the parameter. Under appropriate assumptions, the asymptotic normality of the proposed estimators is studied. The strong uniform convergence rate for the estimators of the error variance function is considered. Also, the asymptotic chi-squared distribution of the empirical log-likelihood ratio statistics is proved. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. Meanwhile, one real data example is provided to illustrate our methods.

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Hong, Shaoxin, Jiancheng Jiang, Xuejun Jiang, and Zhijie Xiao. "Unifying inference for semiparametric regression." Econometrics Journal 24, no. 3 (March 11, 2021): 482–501. http://dx.doi.org/10.1093/ectj/utab005.

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Summary In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty, and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favourable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.

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Callingham, Thomas M., Marius Cautun, Alis J. Deason, Carlos S. Frenk, Wenting Wang, Facundo A. Gómez, Robert J. J. Grand, Federico Marinacci, and Ruediger Pakmor. "The mass of the Milky Way from satellite dynamics." Monthly Notices of the Royal Astronomical Society 484, no. 4 (February 5, 2019): 5453–67. http://dx.doi.org/10.1093/mnras/stz365.

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Abstract We present and apply a method to infer the mass of the Milky Way (MW) by comparing the dynamics of MW satellites to those of model satellites in the eagle cosmological hydrodynamics simulations. A distribution function (DF) for galactic satellites is constructed from eagle using specific angular momentum and specific energy, which are scaled so as to be independent of host halo mass. In this two-dimensional space, the orbital properties of satellite galaxies vary according to the host halo mass. The halo mass can be inferred by calculating the likelihood that the observed satellite population is drawn from this DF. Our method is robustly calibrated on mock eagle systems. We validate it by applying it to the completely independent suite of 30 auriga high-resolution simulations of MW-like galaxies: the method accurately recovers their true mass and associated uncertainties. We then apply it to 10 classical satellites of the MW with six-dimensional phase-space measurements, including updated proper motions from the Gaia satellite. The mass of the MW is estimated to be $M_{200}^{\rm {MW}}=1.17_{-0.15}^{+0.21}\times 10^{12}\, \mathrm{M}_{\odot }$ (68 per cent confidence limits). We combine our total mass estimate with recent mass estimates in the inner regions of the Galaxy to infer an inner dark matter (DM) mass fraction $M^\rm {DM}(\lt 20~\rm {kpc})/M^\rm {DM}_{200}=0.12$, which is typical of ${\sim }10^{12}\, \mathrm{M}_{\odot }$ lambda cold dark matter haloes in hydrodynamical galaxy formation simulations. Assuming a Navarro, Frenk and White (NFW) profile, this is equivalent to a halo concentration of $c_{200}^{\rm {MW}}=10.9^{+2.6}_{-2.0}$.

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6

Bell, Michael J., Wayne Strong, Denis Elliott, and Charlie Walker. "Soil nitrogen—crop response calibration relationships and criteria for winter cereal crops grown in Australia." Crop and Pasture Science 64, no. 5 (2013): 442. http://dx.doi.org/10.1071/cp12431.

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More than 1200 wheat and 120 barley experiments conducted in Australia to examine yield responses to applied nitrogen (N) fertiliser are contained in a national database of field crops nutrient research (BFDC National Database). The yield responses are accompanied by various pre-plant soil test data to quantify plant-available N and other indicators of soil fertility status or mineralisable N. A web application (BFDC Interrogator), developed to access the database, enables construction of calibrations between relative crop yield ((Y0/Ymax) × 100) and N soil test value. In this paper we report the critical soil test values for 90% RY (CV90) and the associated critical ranges (CR90, defined as the 70% confidence interval around that CV90) derived from analysis of various subsets of these winter cereal experiments. Experimental programs were conducted throughout Australia’s main grain-production regions in different eras, starting from the 1960s in Queensland through to Victoria during 2000s. Improved management practices adopted during the period were reflected in increasing potential yields with research era, increasing from an average Ymax of 2.2 t/ha in Queensland in the 1960s and 1970s, to 3.4 t/ha in South Australia (SA) in the 1980s, to 4.3 t/ha in New South Wales (NSW) in the 1990s, and 4.2 t/ha in Victoria in the 2000s. Various sampling depths (0.1–1.2 m) and methods of quantifying available N (nitrate-N or mineral-N) from pre-planting soil samples were used and provided useful guides to the need for supplementary N. The most regionally consistent relationships were established using nitrate-N (kg/ha) in the top 0.6 m of the soil profile, with regional and seasonal variation in CV90 largely accounted for through impacts on experimental Ymax. The CV90 for nitrate-N within the top 0.6 m of the soil profile for wheat crops increased from 36 to 110 kg nitrate-N/ha as Ymax increased over the range 1 to >5 t/ha. Apparent variation in CV90 with seasonal moisture availability was entirely consistent with impacts on experimental Ymax. Further analyses of wheat trials with available grain protein (~45% of all experiments) established that grain yield and not grain N content was the major driver of crop N demand and CV90. Subsets of data explored the impact of crop management practices such as crop rotation or fallow length on both pre-planting profile mineral-N and CV90. Analyses showed that while management practices influenced profile mineral-N at planting and the likelihood and size of yield response to applied N fertiliser, they had no significant impact on CV90. A level of risk is involved with the use of pre-plant testing to determine the need for supplementary N application in all Australian dryland systems. In southern and western regions, where crop performance is based almost entirely on in-crop rainfall, this risk is offset by the management opportunity to split N applications during crop growth in response to changing crop yield potential. In northern cropping systems, where stored soil moisture at sowing is indicative of minimum yield potential, erratic winter rainfall increases uncertainty about actual yield potential as well as reducing the opportunity for effective in-season applications.

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7

Owen, Art. "Empirical Likelihood Ratio Confidence Regions." Annals of Statistics 18, no. 1 (March 1990): 90–120. http://dx.doi.org/10.1214/aos/1176347494.

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8

Royston, Patrick. "Profile Likelihood for Estimation and Confidence Intervals." Stata Journal: Promoting communications on statistics and Stata 7, no. 3 (September 2007): 376–87. http://dx.doi.org/10.1177/1536867x0700700305.

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Normal-based confidence intervals for a parameter of interest are inaccurate when the sampling distribution of the estimate is nonnormal. The technique known as profile likelihood can produce confidence intervals with better coverage. It may be used when the model includes only the variable of interest or several other variables in addition. Profile-likelihood confidence intervals are particularly useful in nonlinear models. The command pllf computes and plots the maximum likelihood estimate and profile likelihood–based confidence interval for one parameter in a wide variety of regression models.

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9

Ionides, E. L., C. Breto, J. Park, R. A. Smith, and A. A. King. "Monte Carlo profile confidence intervals for dynamic systems." Journal of The Royal Society Interface 14, no. 132 (July 2017): 20170126. http://dx.doi.org/10.1098/rsif.2017.0126.

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Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.

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10

Monti, A. "Empirical likelihood confidence regions in time series models." Biometrika 84, no. 2 (June 1, 1997): 395–405. http://dx.doi.org/10.1093/biomet/84.2.395.

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11

HALL, PETER. "On the bootstrap and likelihood-based confidence regions." Biometrika 74, no. 3 (1987): 481–93. http://dx.doi.org/10.1093/biomet/74.3.481.

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12

Minkin, Salomon. "Likelihood-based confidence regions for log-linear models." European Journal of Operational Research 27, no. 2 (October 1986): 229–34. http://dx.doi.org/10.1016/0377-2217(86)90064-0.

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13

Gimenez, Olivier, Rémi Choquet, Laurent Lamor, Paul Scofield, David Fletcher, Jean-Dominique Lebreton, and Roger Pradel. "Efficient profile-likelihood confidence intervals for capture-recapture models." Journal of Agricultural, Biological, and Environmental Statistics 10, no. 2 (June 2005): 184–96. http://dx.doi.org/10.1198/108571105x46462.

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14

Venzon, D. J., and S. H. Moolgavkar. "A Method for Computing Profile-Likelihood-Based Confidence Intervals." Applied Statistics 37, no. 1 (1988): 87. http://dx.doi.org/10.2307/2347496.

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15

Chalmers, R. Philip, Jolynn Pek, and Yang Liu. "Profile-likelihood Confidence Intervals in Item Response Theory Models." Multivariate Behavioral Research 52, no. 5 (June 8, 2017): 533–50. http://dx.doi.org/10.1080/00273171.2017.1329082.

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16

Carpenter, James. "Assessing parameter uncertainty via bootstrap likelihood ratio confidence regions." Journal of Applied Statistics 25, no. 5 (October 1998): 639–49. http://dx.doi.org/10.1080/02664769822873.

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17

Schwetz, Thomas. "Variations on KamLAND: likelihood analysis and frequentist confidence regions." Physics Letters B 577, no. 3-4 (December 2003): 120–28. http://dx.doi.org/10.1016/j.physletb.2003.10.024.

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18

CHEN, ZHENMIN. "OBTAINING POINT ESTIMATORS OF PARAMETERS FROM CONFIDENCE INTERVALS OR JOINT CONFIDENCE REGIONS." International Journal of Reliability, Quality and Safety Engineering 14, no. 01 (February 2007): 21–28. http://dx.doi.org/10.1142/s0218539307002489.

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There are several different ways to obtain point estimators for the parameters of a population distribution. The maximum likelihood estimation and moment estimation are the most commonly used ones. Using point estimators only to estimate unknown parameters is somewhat risky because the probability that the estimation is wrong is almost 100%. Interval estimation, on the other hand, can reduce this risk considerably. The purpose of this paper is to propose a new method for obtaining point estimation of parameters. The point estimators discussed here are obtained by squeezing a confidence interval or joint confidence region of the parameters. The proposed method is easy to use in some cases. The estimators obtained by using this method possess some unbiasedness property. It is also shown that the point estimator obtained by this method is more reasonable than the maximum likelihood estimator when the population distribution is skewed.

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19

Xiao, Yuanhui, Jiawei Liu, and Madhusudan Bhandary. "Profile Likelihood Based Confidence Intervals for Common Intraclass Correlation Coefficient." Communications in Statistics - Simulation and Computation 39, no. 1 (December 8, 2009): 111–18. http://dx.doi.org/10.1080/03610910903324834.

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20

Lang, Joseph B. "Score and profile likelihood confidence intervals for contingency table parameters." Statistics in Medicine 27, no. 28 (December 10, 2008): 5975–90. http://dx.doi.org/10.1002/sim.3391.

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21

Pradhan, Vivek, Sandeep Menon, and Ujjwal Das. "Corrected profile likelihood confidence interval for binomial paired incomplete data." Pharmaceutical Statistics 12, no. 1 (January 2013): 48–58. http://dx.doi.org/10.1002/pst.1551.

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22

Claeskens, Gerda, Bing-Yi Jing, Liang Peng, and Wang Zhou. "Empirical likelihood confidence regions for comparison distributions and ROC curves." Canadian Journal of Statistics 31, no. 2 (June 2003): 173–90. http://dx.doi.org/10.2307/3316066.

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23

Meeker, William Q., and Luis A. Escobar. "Teaching about Approximate Confidence Regions Based on Maximum Likelihood Estimation." American Statistician 49, no. 1 (February 1995): 48. http://dx.doi.org/10.2307/2684811.

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24

Meeker, William Q., and Luis A. Escobar. "Teaching about Approximate Confidence Regions Based on Maximum Likelihood Estimation." American Statistician 49, no. 1 (February 1995): 48–53. http://dx.doi.org/10.1080/00031305.1995.10476112.

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25

Zhu, Lixing, and Liugen Xue. "Empirical likelihood confidence regions in a partially linear single-index model." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68, no. 3 (June 2006): 549–70. http://dx.doi.org/10.1111/j.1467-9868.2006.00556.x.

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26

Tsao, Min. "Bounds on coverage probabilities of the empirical likelihood ratio confidence regions." Annals of Statistics 32, no. 3 (June 2004): 1215–21. http://dx.doi.org/10.1214/009053604000000337.

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27

Xie, Yanmei, and Biao Zhang. "Constrained empirical-likelihood confidence regions in nonignorable covariate-missing data problems." Statistics in Medicine 38, no. 3 (October 11, 2018): 452–79. http://dx.doi.org/10.1002/sim.7987.

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28

Evans, Marc A., Hag-Min Kim, and Timothy E. O'Brien. "An Application of Profile-Likelihood Based Confidence Interval to Capture: Recapture Estimators." Journal of Agricultural, Biological, and Environmental Statistics 1, no. 1 (March 1996): 131. http://dx.doi.org/10.2307/1400565.

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29

Chen, Jian-Shen, and Robert I. Jennrich. "The Signed Root Deviance Profile and Confidence Intervals in Maximum Likelihood Analysis." Journal of the American Statistical Association 91, no. 435 (September 1996): 993–98. http://dx.doi.org/10.1080/01621459.1996.10476969.

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30

Saha, Krishna K., Debaraj Sen, and Chun Jin. "Profile likelihood-based confidence interval for the dispersion parameter in count data." Journal of Applied Statistics 39, no. 4 (April 2012): 765–83. http://dx.doi.org/10.1080/02664763.2011.616581.

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31

Heinze, Georg, Meinhard Ploner, and Jan Beyea. "Confidence intervals after multiple imputation: combining profile likelihood information from logistic regressions." Statistics in Medicine 32, no. 29 (July 19, 2013): 5062–76. http://dx.doi.org/10.1002/sim.5899.

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32

Virtanen, A., and E. Uusipaikka. "Computation of profile likelihood-based confidence intervals for reference limits with covariates." Statistics in Medicine 27, no. 7 (2008): 1121–32. http://dx.doi.org/10.1002/sim.3000.

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33

Knott, Christine E., and Christine Schubert Kabban. "Confidence Interval Comparisons For Probability of Detection On Hit/Miss Data." Materials Evaluation 80, no. 12 (December 1, 2022): 50–65. http://dx.doi.org/10.32548/2022.me-04273.

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Probability of detection (POD) studies for evaluating the capabilities of an inspection system for Air Force aircraft structural components commonly use a Logistic Regression model with a Wald 95% confidence interval. However, hit/miss POD data is distributed as a Binomial, and the sample sizes are commonly too small for Wald’s identically and independently normality distributed assumption to be true. This paper uses a large set of simulated representative hit/miss data to compare and contrast the performance of the four confidence intervals methods: Standard Wald, Modified Wald, Profile Likelihood Ratio, and Profile Modified Likelihood Ratio. Performance is measured in terms of bias and existence of a90/95 with respect to data distribution, sample size, overlap, and evenness. This paper provides guidance and methodology on new POD methods that more reliably and accurately estimate a90/95.

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34

Borisov, Ivan, and Evgeny Metelkin. "Confidence intervals by constrained optimization—An algorithm and software package for practical identifiability analysis in systems biology." PLOS Computational Biology 16, no. 12 (December 21, 2020): e1008495. http://dx.doi.org/10.1371/journal.pcbi.1008495.

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Practical identifiability of Systems Biology models has received a lot of attention in recent scientific research. It addresses the crucial question for models’ predictability: how accurately can the models’ parameters be recovered from available experimental data. The methods based on profile likelihood are among the most reliable methods of practical identification. However, these methods are often computationally demanding or lead to inaccurate estimations of parameters’ confidence intervals. Development of methods, which can accurately produce parameters’ confidence intervals in reasonable computational time, is of utmost importance for Systems Biology and QSP modeling. We propose an algorithm Confidence Intervals by Constraint Optimization (CICO) based on profile likelihood, designed to speed-up confidence intervals estimation and reduce computational cost. The numerical implementation of the algorithm includes settings to control the accuracy of confidence intervals estimates. The algorithm was tested on a number of Systems Biology models, including Taxol treatment model and STAT5 Dimerization model, discussed in the current article. The CICO algorithm is implemented in a software package freely available in Julia (https://github.com/insysbio/LikelihoodProfiler.jl) and Python (https://github.com/insysbio/LikelihoodProfiler.py).

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35

Jaeger, Adam. "Computation of Two- and Three-Dimensional Confidence Regions With the Likelihood Ratio." American Statistician 70, no. 4 (October 1, 2016): 395–98. http://dx.doi.org/10.1080/00031305.2016.1182946.

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36

Weld, Christopher, Andrew Loh, and Lawrence Leemis. "Plotting Likelihood-Ratio-Based Confidence Regions for Two-Parameter Univariate Probability Models." American Statistician 74, no. 2 (May 24, 2019): 156–68. http://dx.doi.org/10.1080/00031305.2018.1564696.

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37

Chen, Song Xi. "On the accuracy of empirical likelihood confidence regions for linear regression model." Annals of the Institute of Statistical Mathematics 45, no. 4 (1993): 621–37. http://dx.doi.org/10.1007/bf00774777.

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38

Yang, Guangren, Xia Cui, and Sumin Hou. "Empirical likelihood confidence regions in the single-index model with growing dimensions." Communications in Statistics - Theory and Methods 46, no. 15 (April 17, 2017): 7562–79. http://dx.doi.org/10.1080/03610926.2016.1157190.

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39

Baklizi, Ayman. "Refined Inference on the Scale Parameter of the Generalized Logistic Distribution Based on Adjusted Profile Likelihood Functions." Symmetry 14, no. 11 (November 10, 2022): 2369. http://dx.doi.org/10.3390/sym14112369.

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We consider inference based on the profile likelihood function for the scale parameter of the generalized logistic distribution. This distribution is a generalization of the logistic distribution, a symmetric distribution like the normal distribution, and it has several applications in various fields. The generalization allows for possible left or right skewness, which makes it more flexible for modeling purposes. Inference procedures based on the profile likelihood of the scale parameter do not perform very well when the sample size is small, therefore, we derived adjustments to the profile likelihood for the generalized logistic distribution using results from higher-order likelihood theory. We obtained an adjustment based on the empirical covariances of certain scores of the profile likelihood function. Another adjustment is derived using ancillary statistics. The performance of the adjustments is investigated for point estimation of the scale parameter of the generalized logistic distribution using the bias and mean squared error criteria. Using an extensive simulation study, we found the adjustments are very successful in reducing the bias and the mean squared error of the maximum profile likelihood estimator in most situations. Moreover, we studied the performance of the profile likelihood ratio test and its adjustments using the criterion of the attainment of nominal sizes. We found that, when the sample size is small, the profile likelihood ratio test has empirical sizes that are highly inflated. Therefore, the test will be invalid in such situations. Simulation results show that the adjusted versions of the profile likelihood produce tests that attain the nominal sizes even for very small samples. This also applies to confidence intervals derived from these tests. In conclusion, both adjustments of the profile likelihood have significantly better performance than the unadjusted profile likelihood and are recommended, especially for small samples. In particular, the adjustment based on ancillary statistics appears to have the best overall performance in all situations considered. We applied the methods in this paper to real data on Carbon fibers.

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Eddy, David M., Vic Hasselblad, and Ross Shachter. "A Bayesian Method for Synthesizing Evidence: The Confidence Profile Method." International Journal of Technology Assessment in Health Care 6, no. 1 (January 1990): 31–55. http://dx.doi.org/10.1017/s0266462300008928.

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This article describes a collection of meta-analysis techniques based on Bayesian statistics for interpreting, adjusting, and combining evidence to estimate parameters and outcomes important to the assessment of health technologies. The result of an analysis by the Confidence Profile Method is a joint posterior probability distribution for the parameters of interest, from which marginal distributions for any particular parameter can be calculated. The method can be used to analyze problems involving a variety of types of outcomes, a variety of measures of effect, and a variety of experimental designs. This article presents the elements necessary for analysis, including prior distributions, likelihood functions, and specific models for experimental designs that include adjustment for biases.

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41

Funatogawa, Takashi, Ikuko Funatogawa, and Akifumi Yafune. "Profile Likelihood-Based Confidence Intervals Using Monte Carlo Integration for Population Pharmacokinetic Parameters." Journal of Biopharmaceutical Statistics 16, no. 2 (March 1, 2006): 193–205. http://dx.doi.org/10.1080/10543400500508861.

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42

Jiang, Yu Ying, and Xiao Feng Zhu. "Weighted-Correct Empirical likelihood for Linear EV Models." Advanced Materials Research 524-527 (May 2012): 3884–87. http://dx.doi.org/10.4028/www.scientific.net/amr.524-527.3884.

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The empirical likelihood inference based weighted correction in linear EV model with missing responses is studied. A weighted-correct empirical likelihood method is developed. It can be shown that the weighted-correct empirical likelihood ratio is asymptotically standard chi-square. The results can be used directly to construct the asymptotic confidence regions of the unknown parameters. The estimation procedure is relatively simple and the estimated efficiency has been greatly improved.

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43

Hu, Xuemei, and Xiaohui Liu. "Empirical likelihood confidence regions for semi-varying coefficient models with linear process errors." Journal of Nonparametric Statistics 25, no. 1 (March 2013): 161–80. http://dx.doi.org/10.1080/10485252.2012.751385.

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44

Shen, Junshan, Kam Chuen Yuen, and Chunling Liu. "Empirical likelihood confidence regions for one- or two- samples with doubly censored data." Computational Statistics & Data Analysis 93 (January 2016): 285–93. http://dx.doi.org/10.1016/j.csda.2015.01.010.

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45

Worms, Julien, and Rym Worms. "Empirical likelihood based confidence regions for first order parameters of heavy-tailed distributions." Journal of Statistical Planning and Inference 141, no. 8 (August 2011): 2769–86. http://dx.doi.org/10.1016/j.jspi.2011.03.002.

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46

Grosvenor, D. P., J. C. King, T. W. Choularton, and T. Lachlan-Cope. "Downslope föhn winds over the Antarctic Peninsula and their effect on the Larsen ice shelves." Atmospheric Chemistry and Physics 14, no. 18 (September 16, 2014): 9481–509. http://dx.doi.org/10.5194/acp-14-9481-2014.

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Abstract. Mesoscale model simulations are presented of a westerly föhn event over the Antarctic Peninsula mountain ridge and onto the Larsen C ice shelf, just south of the recently collapsed Larsen B ice shelf. Aircraft observations showed the presence of föhn jets descending near the ice shelf surface with maximum wind speeds at 250–350 m in height. Surface flux measurements suggested that melting was occurring. Simulated profiles of wind speed, temperature and wind direction were very similar to the observations. However, the good match only occurred at a model time corresponding to ~9 h before the aircraft observations were made since the model föhn jets died down after this. This was despite the fact that the model was nudged towards analysis for heights greater than ~1.15 km above the surface. Timing issues aside, the otherwise good comparison between the model and observations gave confidence that the model flow structure was similar to that in reality. Details of the model jet structure are explored and discussed and are found to have ramifications for the placement of automatic weather station (AWS) stations on the ice shelf in order to detect föhn flow. Cross sections of the flow are also examined and were found to compare well to the aircraft measurements. Gravity wave breaking above the mountain crest likely created a~situation similar to hydraulic flow and allowed föhn flow and ice shelf surface warming to occur despite strong upwind blocking, which in previous studies of this region has generally not been considered. Our results therefore suggest that reduced upwind blocking, due to wind speed increases or stability decreases, might not result in an increased likelihood of föhn events over the Antarctic Peninsula, as previously suggested. The surface energy budget of the model during the melting periods showed that the net downwelling short-wave surface flux was the largest contributor to the melting energy, indicating that the cloud clearing effect of föhn events is likely to be the most important factor for increased melting relative to non-föhn days. The results also indicate that the warmth of the föhn jets through sensible heat flux ("SH") may not be critical in causing melting beyond boundary layer stabilisation effects (which may help to prevent cloud cover and suppress loss of heat by convection) and are actually cancelled by latent heat flux ("LH") effects (snow ablation). It was found that ground heat flux ("GRD") was likely to be an important factor when considering the changing surface energy budget for the southern regions of the ice shelf as the climate warms.

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Yuan, Mingao, and Yue Zhang. "Empirical Likelihood Inference for Partial Functional Linear Regression Models Based on B-spline." International Journal of Statistics and Probability 8, no. 1 (December 24, 2018): 135. http://dx.doi.org/10.5539/ijsp.v8n1p135.

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In this paper, we apply empirical likelihood method to infer for the regression parameters in the partial functional linear regression models based on B-spline. We prove that the empirical log-likelihood ratio for the regression parameters converges in law to a weighted sum of independent chi-square distributions. Our simulation shows that the proposed empirical likelihood method produces more accurate confidence regions in terms of coverage probability than the asymptotic normality method.

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Chen, Si, YaXing Li, JiYae Shin, and TaeWoong Kim. "Constructing confidence intervals of extreme rainfall quantiles using Bayesian, bootstrap, and profile likelihood approaches." Science China Technological Sciences 59, no. 4 (November 10, 2015): 573–85. http://dx.doi.org/10.1007/s11431-015-5951-8.

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Pradhan, Vivek, and Tathagata Banerjee. "Confidence Interval of the Difference of Two Independent Binomial Proportions Using Weighted Profile Likelihood." Communications in Statistics - Simulation and Computation 37, no. 4 (February 27, 2008): 645–59. http://dx.doi.org/10.1080/03610910701767721.

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XUE, Liugen. "Empirical likelihood confidence regions of the parameters in a partially linear single-index model." Science in China Series A 48, no. 10 (2005): 1333. http://dx.doi.org/10.1360/04ys0139.

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