Empirical Bayes Estimation of Parameter of Burr-Type X Model under LINEX and Squared Error Loss Functions

2011 ◽  
Vol 403-408 ◽  
pp. 5273-5277
Author(s):  
Hai Ying Lan
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimate ◽  
Squared Error Loss ◽  
Bayes Estimates ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimate

The Empirical Bayes estimate of the parameter of Burr-type X distribution is contained .The estimate is obtained under squared error loss and Varian’s linear-exponential (LINEX) loss functions, and is compared with corresponding maximum likelihood and Bayes estimates. Finally, a Monte Carlo numerical example is given to illustrate our results.

Data Processing with Computation in Bayes Reliability Analysis for Burr Type X Distribution under Different Loss Functions

2014 ◽  
Vol 978 ◽  
pp. 205-208
Author(s):  
Hui Zhou
Keyword(s):  
Prior Distribution ◽  
Unknown Parameter ◽  
Empirical Bayes ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Squared Error Loss ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimators

This paper studies the estimation of the parameter of Burr Type X distribution. Maximum likelihood estimator is first derived, and then the Bayes and Empirical Bayes estimators of the unknown parameter are obtained under three loss functions, which are squared error loss, LINEX loss and entropy loss functions. The prior distribution of parmeter used in this paper is Gamma distribution. Finally, a Monte Carlo simulation is given to illustrate the application of these estimators.

scholarly journals Empirical Bayes Based on Squared Error Loss and Precautionary Loss Functions in Sequential Sampling Plan

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 51460-51469
Author(s):  
Katechan Jampachaisri ◽  
Khanittha Tinochai ◽  
Saowanit Sukparungsee ◽  
Yupaporn Areepong
Keyword(s):  
Empirical Bayes ◽  
Sequential Sampling ◽  
Sampling Plan ◽  
Loss Functions ◽  
Squared Error Loss ◽  
Sequential Sampling Plan ◽  
Error Loss ◽  
Squared Error

scholarly journals The effect of loss functions on empirical Bayes reliability analysis

1999 ◽  
Vol 4 (6) ◽  
pp. 539-560 ◽  
Author(s):  
Vincent A. R. Camara ◽  
Chris P. Tsokos
Keyword(s):  
Loss Function ◽  
Empirical Bayes ◽  
Reliability Function ◽  
Loss Functions ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Reliability Estimates ◽  
Logarithmic Loss

The aim of the present study is to investigate the sensitivity of empirical Bayes estimates of the reliability function with respect to changing of the loss function. In addition to applying some of the basic analytical results on empirical Bayes reliability obtained with the use of the “popular” squared error loss function, we shall derive some expressions corresponding to empirical Bayes reliability estimates obtained with the Higgins–Tsokos, the Harris and our proposed logarithmic loss functions. The concept of efficiency, along with the notion of integrated mean square error, will be used as a criterion to numerically compare our results.It is shown that empirical Bayes reliability functions are in general sensitive to the choice of the loss function, and that the squared error loss does not always yield the best empirical Bayes reliability estimate.

scholarly journals On empirical Bayes estimation of multivariate regression coefficient

2006 ◽  
Vol 2006 ◽  
pp. 1-18
Author(s):  
R. J. Karunamuni ◽  
L. Wei
Keyword(s):  
Multivariate Regression ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Bayes Estimator ◽  
Bayes Estimation ◽  
Empirical Bayes Estimation ◽  
Squared Error Loss ◽  
Squared Error ◽  
The Mean ◽  
Empirical Bayes Estimator

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression modelY=Xβ+ε, whereYis anm-vector of observations,Xis a knownm×kmatrix,βis an unknownk-vector, andεis anm-vector of unobservable random variables. The problem is squared error loss estimation ofβbased on some “previous” dataY1,…,Ynas well as the “current” data vectorYwhenβis distributed according to some unknown distributionG, whereYisatisfiesYi=Xβi+εi,i=1,…,n. We construct a new empirical Bayes estimator ofβwhenεi∼N(0,σ2Im),i=1,…,n. The performance of the proposed empirical Bayes estimator is measured using the mean squared error. The rates of convergence of the mean squared error are obtained.

scholarly journals Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function

2020 ◽  
Vol 9 (2) ◽  
pp. 38
Author(s):  
Josphat. K. Kinyanjui ◽  
Betty. C. Korir
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Risk Function ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

scholarly journals Bayes Estimation of Two-Phase Linear Regression Model

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Mayuri Pandya ◽  
Krishnam Bhatt ◽  
Paresh Andharia
Keyword(s):  
Regression Model ◽  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Random Errors ◽  
Two Phase ◽  
Inference Problem ◽  
Bayes Estimates ◽  
Linex Loss

Let the regression model be Yi=β1Xi+εi, where εi are i. i. d. N (0,σ2) random errors with variance σ2>0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in slope, regression parameter β2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β1,β2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

Optimal Bayesian point estimates and credible intervals for ranking with application to county health indices

2018 ◽  
Vol 28 (9) ◽  
pp. 2876-2891 ◽  
Author(s):  
Patricia I Jewett ◽  
Li Zhu ◽  
Bin Huang ◽  
Eric J Feuer ◽  
Ronald E Gangnon
Keyword(s):  
Loss Functions ◽  
Pairwise Comparisons ◽  
Typical Application ◽  
Squared Error Loss ◽  
Health Indices ◽  
Error Loss ◽  
Squared Error ◽  
Point Estimates ◽  
Credible Intervals ◽  
Highest Posterior Density

It is fairly common to rank different geographic units, e.g. counties in the USA, based on health indices. In a typical application, point estimates of the health indices are obtained for each county, and the indices are then simply ranked as if they were known constants. Several authors have considered optimal rank estimators under squared error loss on the rank scale as a default method for general purpose ranking, e.g. situations where ranking units across the full spectrum of performance (low, medium, high) is important. While computationally convenient, squared error loss on the rank scale may not represent the true inferential goals of rank consumers. We construct alternative loss functions based on three components: (1) the inferential goal (rank position or pairwise comparisons), (2) the scale (original, log-transformed or rank) and (3) the (positional or pairwise) loss function (0/1, squared error or absolute error). We can obtain optimal ranks for loss functions based on rank positions and nearly optimal ranks for loss functions based on pairwise comparisons paired with highest posterior density (HPD) credible intervals. We compare inferences produced by the various ranking methods, both optimal and heuristic, using low birth weight data for counties in the Midwestern United States, from 2006 to 2012.

Data Processing and Technology Application in Bayes and Empirical Bayes Reliability Analysis of Parameter of Ailamujia Distribution

2014 ◽  
Vol 951 ◽  
pp. 249-252
Author(s):  
Hui Zhou
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Likelihood Estimator ◽  
Empirical Bayesian ◽  
Technology Application ◽  
Inverse Gamma ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimators

The estimation of the parameter of the ЭРланга distribution is discussed based on complete samples. Bayes and empirical Bayesian estimators of the parameter of the ЭРланга distribution are obtained under squared error loss and LINEX loss by using conjugate prior inverse Gamma distribution. Finally, a Monte Carlo simulation example is used to compare the Bayes and empirical Bayes estimators with the maximum likelihood estimator.

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