Bayes Prediction for a Stratified Regression Superpopulation Model Using Balanced Loss Function

We consider the stratified regression superpopulation model and obtain Bayes predictor of the finite population mean under Zellner's two-criterion balanced loss function (BLF). BLF predictor simplifies to a linear combination of the sample and predictive means. Furthermore, it reduces to some of the well-known classical and Bayes predictors. Relative losses and relative savings loss are obtained to investigate loss robustness of the BLF predictor. It is found to perform better than the usual sample mean as well as the predictive mean in the minimal Bayes predictive expected loss sense.     

Bayes Predictor of One-Parameter Exponential Family Type Population Mean Under Balanced Loss Function

We obtain a Bayes predictor and a Bayes prediction risk of the mean of a finite population relative to the balanced loss function. The predictive expected losses associated with classical and standard Bayes predictors are derived and compared with that of a Bayes predictor under a balanced loss function. Specific expressions for a regular exponential family distributed superpopulation are presented and illustrated for some well-known superpopulations.     

A note on finite population prediction under asymetric loss functions

The purpose of the present note is to derive optimal population total predictors relative to the Linex (Zellner, 1986) loss function under some well known superpopulation models. The risk function and Bayes risk are derived and compared with those of usual predictors. Minimax and and admissibility properties of some of the derived predictors are also investigated.     

The Bayes rule of the parameter in (0,1) under Zhang’s loss function with an application to the beta-binomial model

Abstract

For the restricted parameter space (0,1), we propose Zhang’s loss function which satisfies all the 7 properties for a good loss function on (0,1). We then calculate the Bayes rule (estimator), the posterior expectation, the integrated risk, and the Bayes risk of the parameter in (0,1) under Zhang’s loss function. We also calculate the usual Bayes estimator under the squared error loss function, and the Bayes estimator has been proved to underestimate the Bayes estimator under Zhang’s loss function. Finally, the numerical simulations and a real data example of some monthly magazine exposure data exemplify our theoretical studies of two size relationships about the Bayes estimators and the Posterior Expected Zhang’s Losses (PEZLs).     

Comparison of linex and quadratic bayes estimators foe the rayleigh distribution

In this paper, the Bayes estimators for the parameter, the reliability function, and failure rate function of the Rayleigh distribution are obtained when based on complete or type II censored samples. Some types of the linex loss function are used. Comparieons in terms of risks of those under linex loss and squared error loss function with Bayes estimators relative to squared error loss function are made, Numerical example and simulation example are included.     

Bayes prediction of Poisson regression superpopulation mean with a non gamma prior

We consider Khamis' (1960) Laguerre expansion with gamma weight function as a class of “near-gamma” priors (K-prior) to obtain the Bayes predictor of a finite population mean under the Poisson regression superpopulation model using Zellner's balanced loss function (BLF). Kullback–Leibler (K-L) distance between gamma and some K-priors is tabulated to examine the quantitative prior robustness. Some numerical investigations are also conducted to illustrate the effects of a change in skewness and/or kurtosis on the Bayes predictor and the corresponding minimal Bayes predictive expected loss (MBPEL). Loss robustness with respect to the class of BLFs is also examined in terms of relative savings loss (RSL).     

Bayesian Estimation of Regression Coefficients Under Extended Balanced Loss Function

Appreciating the desirability of simultaneously using both the criteria of goodness of fitted model and clustering of estimates around true parameter values, an extended version of the balanced loss function is presented and the Bayesian estimation of regression coefficients is discussed. The thus obtained optimal estimator is then compared with the least squares estimator and posterior mean vector with respect to the criteria like posterior expected loss, Bayes risk, bias vector, mean squared error matrix and risk function.     

Stein rule prediction of the composite target function in a general linear regression model

This paper considers the problem of simultaneous prediction of the actual and average values of the dependent variable in a general linear regression model. Utilizing the philosophy of Stein rule procedure, a family of improved predictors for a linear function of the actual and expected value of the dependent variable for the forecast period has been proposed. An unbiased estimator for the mean squared error (MSE) matrix of the proposed family of predictors has been obtained and dominance of the family of Stein rule predictors over the best linear unbiased predictor (BLUP) has been established under a quadratic loss function.     

Robustness of Bayes Prediction Under Error-in-Variables Superpopulation Model

In this article, we consider Bayes prediction in a finite population under the simple location error-in-variables superpopulation model. Bayes predictor of the finite population mean under Zellner's balanced loss function and the corresponding relative losses and relative savings loss are derived. The prior distribution of the unknown location parameter of the model is assumed to have a non-normal distribution belonging to the class of Edgeworth series distributions. Effects of non normality of the “true” prior distribution and that of a possible misspecification of the loss function on the Bayes predictor are illustrated for a hypothetical population.     

Bayesian Estimation for Poisson-exponential Model under Progressive Type-II Censoring Data with Binomial Removal and Its Application to Ovarian Cancer Data

In this article, we propose Maximum likelihood estimators (MLEs) and Bayes estimators of parameters of Poisson-exponential distribution (PED) under General entropy loss function (GELF) and Squared error loss function (SELF) for Progressive type-II censored data with binomial removals (PT-II CBRs). The MLEs and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from PED. The proposed methodology is illustrated on a real dataset of ovarian cancer.     

Preliminary test and Bayes Estimation of a Location Parameter Under Blinex Loss

In this article, the preliminary test estimator is considered under the BLINEX loss function. The problem under consideration is the estimation of the location parameter from a normal distribution. The risk under the null hypothesis for the preliminary test estimator, the exact risk function for restricted maximum likelihood and approximated risk function for the unrestricted maximum likelihood estimator, are derived under BLINEX loss and the different risk structures are compared to one another both analytically and computationally. As a motivation on the use of BLINEX rather than LINEX, the risk for the preliminary test estimator under BLINEX loss is compared to the risk of the preliminary test estimator under LINEX loss and it is shown that the LINEX expected loss is higher than BLINEX expected loss. Furthermore, two feasible Bayes estimators are derived under BLINEX loss, and a feasible Bayes preliminary test estimator is defined and compared to the classical preliminary test estimator.     

Inference for the software reliability using asymmetric los fimctions:a hierarchical bayes approach

The aim of this paper is to propose a hierarchical Bayes approach and an appropriate loss function to perform a Bayesian analysis of the total number of software failures denoted by N. It is shown that the Bayes procedure is more stable than the maximum likelihood procedure and a stopping rule for debugging the software is suggested via the LIN EX loss function.     

On Bayes Linear Unbiased Estimator Under the Balanced Loss Function

In this paper, the Bayes linear unbiased estimator (Bayes LUE) is derived under the balanced loss function. Moreover, the superiority of Bayes LUE over ordinary least square estimator is studied under the mean square error matrix criterion and Pitman closeness criterion. Furthermore, we compare Bayes LUE under the balanced loss function with Bayes LUE under the quadratic loss function.     

On the Bayes estimators of the parameters of size-biased generalized power series distributions

ABSTRACT

In this paper, we derive the Bayes estimators of functions of parameters of the size-biased generalized power series distribution under squared error loss function and weighted square error loss function. The results of size-biased GPSD are then used to obtain particular cases of the size-biased negative binomial, size-biased logarithmic series, and size-biased Poisson distributions. These estimators are better than the classical minimum variance unbiased estimators in the sense that they increase the range of the estimation. Finally, an example is provided to illustrate the results and a goodness of fit test is done using the maximum likelihood and Bayes estimators.     

Curtailed Bayesian sampling plans for exponential distributions based on Type-II censored samples

This paper studies the problem of designing a curtailed Bayesian sampling plan (CBSP) with Type-II censored data. We first derive the Bayesian sampling plan (BSP) for exponential distributions based on Type-II censored samples in a general loss function. For the conjugate prior with quadratic loss function, an explicit expression for the Bayes decision function is derived. Using the property of monotonicity of the Bayes decision function, a new Bayesian sampling plan modified by the curtailment procedure, called a CBSP, is proposed. It is shown that the risk of CBSP is less than or equal to that of BSP. Comparisons among some existing BSPs and the proposed CBSP are given. Monte Carlo simulations are conducted, and numerical results indicate that the CBSP outperforms those early existing sampling plans if the time loss is considered in the loss function.     

Bayes Estimator of Inverse Gaussian Parameters Under General Entropy Loss Function Using Lindley's Approximation

In this article, we obtained Bayes estimators of parameters of Inverse Gaussian distributions under asymmetric loss function using Lindley's Approximation (L-Approximation). The proposed estimators have been compared with the corresponding estimators obtained under symmetric loss function and MLE for their risks. This comparison is illustrated using Monte-Carlo study of 2,000 simulated sample from the Inverse Gaussian distribution.     

Bayesian multivariate normal analysis under the extended reflected normal loss function

This paper considers the Bayesian analysis of the multivariate normal distribution under a new and bounded loss function, based on a reflection of the multivariate normal density function. The Bayes estimators of the mean vector can be derived for an arbitrary prior distribution of [d]. When the covariance matrix has an inverted Wishart prior density, a Bayes estimator of[d] is obtained under a bounded loss function, based on the entropy loss. Finally the admissibility of all linear estimators c[d]+ d for the mean vector is considered     

Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution. Now deceased.     

Bayesian and Non Bayesian Estimations on the Exponentiated Modified Weibull Distribution for Progressive Censored Sample

The four-parameter Exponentiated Modified Weibull (EMW) is considered as an important lifetime distribution. Based on progressive Type-II censored sample, maximum likelihood and Bayesian estimators of the parameters, reliability function, and hazard rate function are derived. Two cases are considered: first, the case of one unknown exponent parameter of EMW and second, the case when two parameters of the EMW are both unknown. The Bayes estimators are studied under squared error and LINEX loss functions. The standard Bayes and importance sampling are considered for the estimation. Monte Carlo simulations are performed under different samples sizes and different censoring schemes for investigating and comparing the methods of estimation.     

Sufficient conditions for the admissibility under the LINEX loss function in non-regular case

Consider an estimation problem under the LINEX loss function in one-parameter non-regular distributions where the endpoint of the support depends on an unknown parameter. The purpose of this paper is to give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible. Also, it is shown that the main result in this paper is an extension of the quadratic loss case. Some examples are given.