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Journal articles on the topic 'Estimating function'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 February 2023

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1

Liang, Y., A. Thavaneswaran, and B. Abraham. "Joint Estimation Using Quadratic Estimating Function." Journal of Probability and Statistics 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/372512.

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A class of martingale estimating functions is convenient and plays an important role for inference for nonlinear time series models. However, when the information about the first four conditional moments of the observed process becomes available, the quadratic estimating functions are more informative. In this paper, a general framework for joint estimation of conditional mean and variance parameters in time series models using quadratic estimating functions is developed. Superiority of the approach is demonstrated by comparing the information associated with the optimal quadratic estimating function with the information associated with other estimating functions. The method is used to study the optimal quadratic estimating functions of the parameters of autoregressive conditional duration (ACD) models, random coefficient autoregressive (RCA) models, doubly stochastic models and regression models with ARCH errors. Closed-form expressions for the information gain are also discussed in some detail.

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2

Thavaneswaran, Aerambamoorthy, Saumen Mandal, and Dharini Pathmanathan. "Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions." International Journal of Statistics and Probability 5, no. 3 (2016): 1. http://dx.doi.org/10.5539/ijsp.v5n3p1.

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There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

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3

Miura, Keiji, Masato Okada, and Shun-ichi Amari. "Estimating Spiking Irregularities Under Changing Environments." Neural Computation 18, no. 10 (2006): 2359–86. http://dx.doi.org/10.1162/neco.2006.18.10.2359.

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We considered a gammadistribution of interspike intervals as a statistical model for neuronal spike generation. A gamma distribution is a natural extension of the Poisson process taking the effect of a refractory period into account. The model is specified by two parameters: a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes over time, observed data are generated from a model with a time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We obtained an optimal estimating function analytically for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation. We suggest a measure of spiking irregularity based on the estimating function, which may be useful for characterizing individual neurons in changing environments.

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4

Zhang, Yunyi, Jiazheng Liu, Zexin Pan, and Dimitris N. Politis. "Estimating transformation function." Electronic Journal of Statistics 13, no. 2 (2019): 3095–119. http://dx.doi.org/10.1214/19-ejs1603.

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5

Mortici, Cristinel. "Estimating gamma function by digamma function." Mathematical and Computer Modelling 52, no. 5-6 (2010): 942–46. http://dx.doi.org/10.1016/j.mcm.2010.05.030.

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6

Tong, Tiejun, Yanyuan Ma, and Yuedong Wang. "Optimal variance estimation without estimating the mean function." Bernoulli 19, no. 5A (2013): 1839–54. http://dx.doi.org/10.3150/12-bej432.

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7

Hu, Feifang, and John D. Kalbfleisch. "The estimating function bootstrap." Canadian Journal of Statistics 28, no. 3 (2000): 449–81. http://dx.doi.org/10.2307/3315958.

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8

Kundu, Piyali, Somesh Kumar, and Kashinath Chatterjee. "Estimating the Reliability Function." Calcutta Statistical Association Bulletin 67, no. 3-4 (2015): 143–61. http://dx.doi.org/10.1177/0008068320150304.

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9

Roy, R., P. Souchoroukov, and T. Griggs. "Function-based cost estimating." International Journal of Production Research 46, no. 10 (2008): 2621–50. http://dx.doi.org/10.1080/00207540601094440.

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10

Peszek, Iza, and Andrew L. Rukhin. "Estimating lognormal hazard function." Journal of Statistical Planning and Inference 41, no. 3 (1994): 281–90. http://dx.doi.org/10.1016/0378-3758(94)90024-8.

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11

Wang, M. "Adjusted profile estimating function." Biometrika 90, no. 4 (2003): 845–58. http://dx.doi.org/10.1093/biomet/90.4.845.

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12

van de Geer, Sara. "Estimating a Regression Function." Annals of Statistics 18, no. 2 (1990): 907–24. http://dx.doi.org/10.1214/aos/1176347632.

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13

Zhou, Chang Hong. "Application of Function Point Estimating." Applied Mechanics and Materials 644-650 (September 2014): 3357–60. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.3357.

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Function point estimating is an important method for system of effort estimation. This article is based on a telecommunication surveillance module system-integrated monitoring module as example. It explains how this estimation method is applied in the project measurement process in detail.Function Point AnalysisFunction point analysis evaluates the functionality of a software system from the software end users perspective. Software functionality comes down to five basic functional elements[1], two of which represent end user demand for data: internal logical files (ILF) and external interface files (EIF). The other three are data gathering and processing features: external inputs (EI), external outputs (EO), external inquiries (EQ)[2].To determine the complexity of each functional element, the following data items are defined: record element type (RET), file type referenced, (FTR), data e1ement type (DET)[3]. To determine all functionalities complexity level, each data and transactional capabilities is assigned with low, average and high level based on standard matrix, see table 1 complexity matrix[4]. After determining the complexity of each feature, using the complexity value defined in table 2[5] multiply by the corresponding function point counts, accumulate to get the totals.Table 1: complexity matrixTable 2: IFPUG unadjusted function point basis

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14

Hovorka, Roman. "Estimating Relative Input Function from Response Function." IFAC Proceedings Volumes 30, no. 2 (1997): 265–70. http://dx.doi.org/10.1016/s1474-6670(17)44582-4.

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15

Qi, Jianming, Fanning Meng, and Wenjun Yuan. "Growth of Meromorphic Function Sharing Functions and Some Uniqueness Problems." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/6250867.

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Estimating the growth of meromorphic solutions has been an important topic of research in complex differential equations. In this paper, we devoted to considering uniqueness problems by estimating the growth of meromorphic functions. Further, some examples are given to show that the conclusions are meaningful.

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16

Mohammed Ahmed, Dr Al Omari. "Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction." Academic Journal of Applied Mathematical Sciences, no. 72 (March 6, 2021): 106–12. http://dx.doi.org/10.32861/ajams.72.106.112.

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This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

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17

Yip, Paul S. F., Daniel Y. T. Fong, and Kenneth Wilson. "Estimating population size by recapture sampling via estimating function." Communications in Statistics. Stochastic Models 9, no. 2 (1993): 179–93. http://dx.doi.org/10.1080/15326349308807261.

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18

Fourdrinier, D., and P. Lepelletier. "Estimating a general function of a quadratic function." Annals of the Institute of Statistical Mathematics 60, no. 1 (2006): 85–119. http://dx.doi.org/10.1007/s10463-006-0072-6.

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19

Sjöberg, Staffan, S. Hellsten, T. Almén, K. Golman, and T. Grönberg. "Estimating Kidney Function during Urography." Acta Radiologica 28, no. 5 (1987): 587–92. http://dx.doi.org/10.3109/02841858709177406.

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20

Sjoberg, S., S. Hellsten, T. Almen, K. Golman, and T. Grönberg. "Estimating Kidney Function during Urography." Acta Radiologica 28, no. 5 (1987): 587–92. http://dx.doi.org/10.1177/028418518702800517.

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Blood samples were taken from 21 subjects at 2 to 4 hours after simultaneous injection of contrast medium (metrizoate) for urography and 51Cr-EDTA. Clearance calculations were performed using the single injection (single slope) technique. The plasma concentrations of 51Cr-EDTA and contrast medium were measured by gamma counting and X-ray fluorescence analysis, respectively. A good correlation was found between the clearance of 51Cr-EDTA and clearance of contrast medium (r=0.94).

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21

Jennings, T. "Estimating the fault rate function." IBM Systems Journal 31, no. 2 (1992): 300–312. http://dx.doi.org/10.1147/sj.312.0300.

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22

Bala, Mohan V., and Josephine Mauskopf. "ESTIMATING THE BAYESIAN LOSS FUNCTION." International Journal of Technology Assessment in Health Care 17, no. 1 (2001): 27–37. http://dx.doi.org/10.1017/s0266462301104046.

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Current health economic literature does not provide clear guidelines on how uncertainty around cost-effectiveness estimates should be incorporated into economic decision models. Bayesian analysis is a promising alternative to classical statistics for incorporating uncertainty in economic analysis. Estimating a loss function that relates outcomes to societal welfare is a key component of Bayesian decision analysis. Health economists commonly compute the loss function based on the quality-adjusted life-years associated with each outcome. However, if welfare economics is adopted as the theoretical foundation of the analysis, a loss function based in cost-benefit analysis (CBA) may be more appropriate. CBA has not found wide use in health economics due to practical issues associated with estimating such a loss function. In this paper, we present a method based in conjoint analysis for estimating the CBA loss function that can be applied in practice. We illustrate the use of the methodology using data from a pilot study.

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23

Di Rienzo, M., P. Castiglioni, G. Mancia, A. Pedotti, and G. Parati. "Advancements in estimating baroreflex function." IEEE Engineering in Medicine and Biology Magazine 20, no. 2 (2001): 25–32. http://dx.doi.org/10.1109/51.917721.

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24

Dong, Ning, and Hua-Guo Xu. "Estimating Renal Function in Pregnancy." JAMA 321, no. 21 (2019): 2136. http://dx.doi.org/10.1001/jama.2019.3614.

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25

Adhya, Sumanta. "Bootstrap Variance Estimation for Semiparametric Finite Population Distribution Function Estimator." Calcutta Statistical Association Bulletin 70, no. 1 (2018): 17–32. http://dx.doi.org/10.1177/0008068318765583.

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Estimating finite population distribution function (FPDF) emerges as an important problem to the survey statisticians since the pioneering work of Chambers and Dunstan [1] . It unifies estimation of standard finite population parameters, namely, mean and quantiles. Regarding this, estimating variance of FPDF estimator is an important task for accessing the quality of the estimtor and drawing inferences (e.g., confidence interval estimation) on finite population parameters. Due to non-linearity of FPDF estimator, resampling-based methods are developed earlier for parametric or non-parametric Chambers–Dunstan estimator. Here, we attempt the problem of estimating variance of P-splines-based semiparametric model-based Chambers–Dunstan type estimator of the FPDF. The proposed variance estimator involes bootstrapping. Here, the bootstrap procedure is non-trivial since it does not imitate the full mechanism of two-stage sample generating procedure from an infinite hypothetical population (superpopulation). We have established the weak consistency of the proposed resampling-based variance estimator for specific sampling designs, e.g., simple random sampling. Also, the satisfactory empirical performance of the poposed estimator has been shown through simulation studies and a real life example.

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26

Chaturvedi, Ajit, and Anupam Pathak. "Estimating the Reliability Function for a Family of Exponentiated Distributions." Journal of Probability and Statistics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/563093.

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A family of exponentiated distributions is proposed. The problems of estimating the reliability function are considered. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are derived. A comparative study of the two methods of estimation is done. Simulation study is preformed.

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27

Zieliński, Ryszard. "Estimating quantiles with Linex loss function. Applications to VaR estimation." Applicationes Mathematicae 32, no. 4 (2005): 367–73. http://dx.doi.org/10.4064/am32-4-1.

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28

Busu, Cristian, and Mihail Busu. "An Application of the Kalman Filter Recursive Algorithm to Estimate the Gaussian Errors by Minimizing the Symmetric Loss Function." Symmetry 13, no. 2 (2021): 240. http://dx.doi.org/10.3390/sym13020240.

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Kalman filtering is a linear quadratic estimation (LQE) algorithm that uses a time series of observed data to produce estimations of unknown variables. The Kalman filter (KF) concept is widely used in applied mathematics and signal processing. In this study, we developed a methodology for estimating Gaussian errors by minimizing the symmetric loss function. Relevant applications of the kinetic models are described at the end of the manuscript.

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29

Fahmy, Nermin. "Estimating hazard rates using appropriate statistical distribution." International Journal of Advanced Statistics and Probability 6, no. 1 (2017): 18. http://dx.doi.org/10.14419/ijasp.v6i1.8358.

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This research deals primarily with the hazard rate function of a class of distributions, and discusses the relation between the hazard rate function, and the density function. It was found that the Makeham-Gompertz mortality distribution and the truncated extreme value distribution had the same hazard rate function. We used the hazard rate function derived from these distributions to find the actuarial functions.

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30

Al-Duais, Fuad S. "Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values." Complexity 2021 (April 26, 2021): 1–7. http://dx.doi.org/10.1155/2021/9982916.

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The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability.

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31

Morrissey, Mark L., Werner E. Cook, and J. Scott Greene. "An Improved Method for Estimating the Wind Power Density Distribution Function." Journal of Atmospheric and Oceanic Technology 27, no. 7 (2010): 1153–64. http://dx.doi.org/10.1175/2010jtecha1390.1.

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Abstract The wind power density (WPD) distribution curve is essential for wind power assessment and wind turbine engineering. The usual practice of estimating this curve from wind speed data is to first estimate the wind speed probability density function (PDF) using a nonparametric or parametric method. The density function is then multiplied by one-half the wind speed cubed times the air density. Unfortunately, this means that minor errors in the estimation of the wind speed PDF can result in large errors in the WPD distribution curve because the cubic term in the WPD function magnifies the error. To avoid this problem, this paper presents a new method of estimating the WPD distribution curve through a direct estimation of the curve using a Gauss–Hermite expansion. It is demonstrated that the proposed method provides a much more reliable estimate of the WPD distribution curve.

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32

Bonat, Wagner H., Ricardo R. Petterle, John Hinde, and Clarice GB Demétrio. "Flexible quasi-beta regression models for continuous bounded data." Statistical Modelling 19, no. 6 (2018): 617–33. http://dx.doi.org/10.1177/1471082x18790847.

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We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions. The mean structure is modelled by means of a link function and a linear predictor, while the mean and variance relationship has the form [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the mean, dispersion and power parameters respectively. The models are fitted by using an estimating function approach where the quasi-score and Pearson estimating functions are employed for the estimation of the regression and dispersion parameters respectively. The flexible quasi-beta regression model can automatically adapt to the underlying bounded data distribution by the estimation of the power parameter. Furthermore, the model can easily handle data with exact zeroes and ones in a unified way and has the Bernoulli mean and variance relationship as a limiting case. The computational implementation of the proposed model is fast, relying on a simple Newton scoring algorithm. Simulation studies, using datasets generated from simplex and beta regression models show that the estimating function estimators are unbiased and consistent for the regression coefficients. We illustrate the flexibility of the quasi-beta regression model to deal with bounded data with two examples. We provide an R implementation and the datasets as supplementary materials.

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33

Robert, Christian Y. "Estimating the multivariate extremal index function." Bernoulli 14, no. 4 (2008): 1027–64. http://dx.doi.org/10.3150/08-bej145.

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34

Hornum, Mads, Morten Baltzer Houlind, Esben Iversen, et al. "Estimating Renal Function Following Lung Transplantation." Journal of Clinical Medicine 11, no. 6 (2022): 1496. http://dx.doi.org/10.3390/jcm11061496.

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Background: Patients undergoing lung transplantation (LTx) experience a rapid decline in glomerular filtration rate (GFR) in the acute postoperative period. However, no prospective longitudinal studies directly comparing the performance of equations for estimating GFR in this patient population currently exist. Methods: In total, 32 patients undergoing LTx met the study criteria. At pre-LTx and 1-, 3-, and 12-weeks post-LTx, GFR was determined by 51Cr-EDTA and by equations for estimating GFR based on plasma (P)-Creatinine, P-Cystatin C, or a combination of both. Results: Measured GFR declined from 98.0 mL/min/1.73 m2 at pre-LTx to 54.1 mL/min/1.73 m2 at 12-weeks post-LTx. Equations based on P-Creatinine underestimated GFR decline after LTx, whereas equations based on P-Cystatin C overestimated this decline. Overall, the 2021 CKD-EPI combination equation had the lowest bias and highest precision at both pre-LTx and post-LTx. Conclusions: Caution must be applied when interpreting renal function based on equations for estimating GFR in the acute postoperative period following LTx. Simplified methods for measuring GFR may allow for more widespread use of measured GFR in this vulnerable patient population.

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35

Fujii, Yoshinori. "ON HOMOGENEITY TEST USING ESTIMATING FUNCTION." Bulletin of informatics and cybernetics 26, no. 1/2 (1994): 101–7. http://dx.doi.org/10.5109/13436.

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36

Lin, Lu. "Maximum Information and Optimum Estimating Function." Chinese Annals of Mathematics 24, no. 03 (2003): 349–58. http://dx.doi.org/10.1142/s0252959903000359.

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37

Kanai, Hiroomi, Hiroaki Ogata, and Masanobu Taniguchi. "Estimating function approach for CHARN Models." METRON 68, no. 1 (2010): 1–21. http://dx.doi.org/10.1007/bf03263521.

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38

Kim, Jong-Tae, Chang-Ha Hwang, Hye-Jung Park, and Joo-Yong Shim. "Estimating Variance Function with Kernel Machine." Communications for Statistical Applications and Methods 16, no. 2 (2009): 383–88. http://dx.doi.org/10.5351/ckss.2009.16.2.383.

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39

Mammen, Enno. "Estimating a Smooth Monotone Regression Function." Annals of Statistics 19, no. 2 (1991): 724–40. http://dx.doi.org/10.1214/aos/1176348117.

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40

Carstensen, Kai. "Estimating the ECB Policy Reaction Function." German Economic Review 7, no. 1 (2006): 1–34. http://dx.doi.org/10.1111/j.1468-0475.2006.00145.x.

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Abstract This paper estimates the policy reaction function of the European Central Bank in the first four years of EMU using an ordered probit model which accounts for the fact that central bank rates are set at multiples of 25 basis points. Starting from a baseline model which mimics the Taylor rule, the impacts of different economic variables on interest rate decisions are analysed. It is concluded that the monetary growth measure which was announced by the ECB as the first pillar of their monetary strategy does not play an outstanding role for the actual interest rate decisions. More sophisticated measures like the money overhang which uses information from both pillars are better suited. Overall, it is concluded that the revision of the monetary policy strategy in May 2003 which implied a downgrading of the first pillar will not induce any observable changes in monetary policy decisions.

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41

Linden, Mikael. "Estimating effort function with semiparametric model." Computational Statistics 14, no. 4 (1999): 501–13. http://dx.doi.org/10.1007/s001800050028.

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42

Harel, Ziv, and Joel G. Ray. "Estimating Renal Function in Pregnancy—Reply." JAMA 321, no. 21 (2019): 2136. http://dx.doi.org/10.1001/jama.2019.3618.

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43

Yuan, Wenfa, Dongli Chen, and Huiguang Kang. "Estimation of derivatives for regular positive real part functions." Tamkang Journal of Mathematics 36, no. 3 (2005): 193–97. http://dx.doi.org/10.5556/j.tkjm.36.2005.111.

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In this paper, we mainly discuss the problem of estimating the $n$th derivative of regular positive real part functions: $ g(z)=c_0+c_1z+\cdots+c_nz^n+\cdots $, which is regular in $ |z|0 $. With the principle of inductive method and the characters of regular positive real part functions, the estimation of the $n$th derivative for the function $ g(z) $ is presented. The derivative estimation for positive functions with real part has been solved completely.

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44

Zhu, Hong Jun. "Value Engineering-Oriented Approach to Evaluating Conceptual Design Schemes of Sugarcane Harvester." Advanced Materials Research 468-471 (February 2012): 1300–1307. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.1300.

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In order to improve agricultural machinery product value in conceptual design scheme evaluation, a novel approach was put forward to evaluate conceptual design schemes in the view of value engineering. Realization of the method was divided into cost estimation and function evaluation. In cost estimation, weighted mahalanobis distance between historical data and estimating product schemes were calculated to express their similarity, their cost attributes were described by different membership functions, exponential smoothing method was selected to get estimation solution; in function evaluation, evaluation assignment was chosen to determine function coefficients of different schemes, by using improved AHP to modify judgment matrix. An example of sugarcane harvester is given to illustrate the validity and feasibility of proposed method.

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45

Salih, Makki A. Mohammed, and Zainab Saddi Noori. "Using Simulation to Estimate Reliability Function for Generalized Inverse Weibull Distribution." Journal of Physics: Conference Series 2322, no. 1 (2022): 012013. http://dx.doi.org/10.1088/1742-6596/2322/1/012013.

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Abstract In this paper, we estimating three parameters (α, α, θ) of the generalized inverse Weibull distribution, and the reliability function, by using four estimation methods which are each of Moments (MOM), Modification of Moments (MM), Percentile (PER) and Maximum Likelihood estimation (MLE), the simulation technique was used to generate the random variable for this estimate. Finally, comparisons were made between the obtained results from the estimators using the mean square error. By analyzing the results, the following is revealed: For the α parameter, it turns out that α ^ M M and α ^ M L E are better than other estimators, as for the β parameter, the results were shown β ^ P E R is the best, but the results of θ parameter showed that θ ^ M L E is the best, and for estimating reliability that R ^ M L E is the best.

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46

Durairajan, T. M., and Martin L. William. "Optimal estimating function for estimation and prediction in semi-parametric models." Journal of Statistical Planning and Inference 138, no. 10 (2008): 3283–92. http://dx.doi.org/10.1016/j.jspi.2008.01.009.

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47

Hall, Peter, and R. J. Carroll. "Variance Function Estimation in Regression: The Effect of Estimating the Mean." Journal of the Royal Statistical Society: Series B (Methodological) 51, no. 1 (1989): 3–14. http://dx.doi.org/10.1111/j.2517-6161.1989.tb01744.x.

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48

Zhang, Shunpu, Zhong Li, and Zhiying Zhang. "Estimating a Distribution Function at the Boundary." Austrian Journal of Statistics 49, no. 1 (2020): 1–23. http://dx.doi.org/10.17713/ajs.v49i1.801.

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Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

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49

Nogales, Agustín G. "Optimal Bayesian Estimation of a Regression Curve, a Conditional Density, and a Conditional Distribution." Mathematics 10, no. 8 (2022): 1213. http://dx.doi.org/10.3390/math10081213.

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Abstract:

In this paper, several related estimation problems are addressed from a Bayesian point of view, and optimal estimators are obtained for each of them when some natural loss functions are considered. The problems considered are the estimation of a regression curve, a conditional distribution function, a conditional density, and even the conditional distribution itself. These problems are posed in a sufficiently general framework to cover continuous and discrete, univariate and multivariate, and parametric and nonparametric cases, without the need to use a specific prior distribution. The loss functions considered come naturally from the quadratic error loss function commonly used in estimating a real function of the unknown parameter. The cornerstone of these Bayes estimators is the posterior predictive distribution. Some examples are provided to illustrate the results.

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Färe, Rolf, Dimitris Margaritis, Paul Rouse, and Israfil Roshdi. "Estimating the hyperbolic distance function: A directional distance function approach." European Journal of Operational Research 254, no. 1 (2016): 312–19. http://dx.doi.org/10.1016/j.ejor.2016.03.045.

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