A note on new feasible generalized ridge regression estimator under the linex loss function

In this paper, using the asymmetric LINEX loss function we derive and numerically evaluate the risk function of the new feasible ridge regression estimator.We also examine the risk performance of this estimator when the LINEX loss function is used.     

Bayesian estimation for non zero inflated modified power series distribution under linex and generalized entropy loss functions

Abstract

In this paper, we derive Bayesian estimators of the parameters of modified power series distributions inflated at any of a support point under linex and general entropy loss function. We assume that the prior information can be summarized by a uniform, Beta, two-sided power, Gamma or generalized Pareto distributions. The obtained results are demonstrated on the generalized Poisson and the generalized negative binomial distribution inflated at a given point.     

Testimator of the scale parameter of the exponential distribution using linex loss function

The present paper investigates the properties of a testimator of scale of an exponential distribution under Linex loss function. The risk function of testimator is derived and compared with that of an admissible estimator relative to Linex loss function. The shrinkage testimator is proposed which is the extension of testimator and its properties have been discussed. The level of significance of testimator is decided on the basis of Akaike information criterion following Hirano (1977, 1978). It is found that the testimator and shrinkage testimator dominates the admissible estimator in terms of risk in certain parametric space.     

A family of shrinkage estimators for the square of mean in normal distribution

This paper is devoted to the problem of estimating the square of population mean (μ²) in normal distribution when a prior estimate or guessed value σ₀ ² of the population variance σ² is available. We have suggested a family of shrinkage estimators , say, for μ² with its mean squared error formula. A condition is obtained in which the suggested estimator is more efficient than Srivastava et al’s (1980) estimator T_min. Numerical illustrations have been carried out to demonstrate the merits of the constructed estimator over T_min. It is observed that some of these estimators offer improvements over T_min particularly when the population is heterogeneous and σ² is in the vicinity of σ₀ ².     

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.     

Empirical bayes estimation of the mean in a multivariate normal distribution

We consider the problem of estimating the mean vector of a multivariate normal distribution under a variety of assumed structures among the parameters of the sampling and prior distributions. We adopt a pragmatic approach. We adopt distributional familites, assess hyperparmeters, and adopt patterned mean and coveariance structures when it is relatively simple to do so; alternatively, we use the sample data to estimate hyperparameters of prior distributions when assessment is a formidable task; such as the task of assessing parameters of multidimensional problems. James-Stein-like estimators are found to result. In some cases, we've been abl to show that the estimators proposed uniformly dominate the MLE's when measured with respect to quadratic loss functions.     

Three-stage and accelerated sequential point estimation of the normal mean using LINEX loss function

Consider a normal population with unknown mean μ and unknown variance σ². We estimate μ under an asymmetric LINEX loss function such that the associated risk is bounded from above by a known quantity w. This necessitates the use of a random number (N) of observations. Under a fairly broad set of assumptions on N, we derive the asymptotic second-order expansion of the associated risk function. Some examples have been included involving accelerated sequential and three-stage sampling techniques. Performance comparisons of these procedures are considered using a Monte-Carlo study.     

三个多元正态总体在简单半序约束下均值估计

 多元保序回归理论对统计学中研究多维参数在序约束下的估计理论起着关键性作用。本文讨论了当协方差矩阵已知,在简单半序约束下,对三个多元正态总体均值的估计问题,给出了估计的算法。并证明了在多元均方损失条件下,给出的均值估计优于无序约束的均值估计。     

Simultaneous estimation of the multivariate normal mean under balanced loss function

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function which is defined as follows:

where 0 < w < 1 and for i = 1,…,p and j = 1,…,n, X_ij is distributed as normal with mean θi and variance 1. It is shown that the sample mean, X, is admissible when p <3. For p ≥3, we obtain that James-Stein type estimator which has uniformly smaller risk than that of sample mean X.     

On robust Bayesian estimation under some asymmetric and bounded loss function

The problem of Bayesian and robust Bayesian estimation with some bounded and asymmetric loss function ABL is considered for various models. The prior distribution is not exactly specified and covers the conjugate family of prior distributions. The posterior regret, most robust and conditional Γ-minimax estimators are constructed and a preliminary comparison with square-error loss and LINEX loss is presented.     

Bayesian estimation of the generalized lognormal distribution using objective priors

The generalized lognormal distribution plays an important role in analysing data from different life testing experiments. In this paper, we consider Bayesian analysis of this distribution using various objective priors for the model parameters. Specifically, we derive expressions for the Jeffreys-type priors, the reference priors with different group orderings of the parameters, and the first-order matching priors. We also study the properties of the posterior distributions of the parameters under these improper priors. It is shown that only two of them result in proper posterior distributions. Numerical simulation studies are conducted to compare the performances of the Bayesian estimators under the considered priors and the maximum likelihood estimates. Finally, a real-data application is also provided for illustrative purposes.     

A class of Shrunken estimators for normal mean

This paper presents a class of estimators for the mean of a normal population and determines the conditions on characterizing scalars under which the class of estimators uniformly dominates over the conventional sample mean according to the mean-square-error criterion.     

Empirical Bayes estimation for the mean of the selected normal population when there are additional data

ABSTRACT

This paper is concerned with the problem of estimation for the mean of the selected population from two normal populations with unknown means and common known variance in a Bayesian framework. The empirical Bayes estimator, when there are available additional observations, is derived and its bias and risk function are computed. The expected bias and risk of the empirical Bayes estimator and the intuitive estimator are compared. It is shown that the empirical Bayes estimator is asymptotically optimal and especially dominates the intuitive estimator in terms of Bayes risk, with respect to any normal prior. Also, the Bayesian correlation between the mean of the selected population (random parameter) and some interested estimators are obtained and compared.     

Bayesian estimation of reliability using time-to-failure distribution of parametric degradation models

This paper focusses on computing the Bayesian reliability of components whose performance characteristics (degradation – fatigue and cracks) are observed during a specified period of time. Depending upon the nature of degradation data collected, we fit a monotone increasing or decreasing function for the data. Since the components are supposed to have different lifetimes, the rate of degradation is assumed to be a random variable. At a critical level of degradation, the time to failure distribution is obtained. The exponential and power degradation models are studied and exponential density function is assumed for the random variable representing the rate of degradation. The maximum likelihood estimator and Bayesian estimator of the parameter of exponential density function, predictive distribution, hierarchical Bayes approach and robustness of the posterior mean are presented. The Gibbs sampling algorithm is used to obtain the Bayesian estimates of the parameter. Illustrations are provided for the train wheel degradation data.     

An estimator of the common mean of two normal populations

In this paper we consider the estimation of the common mean of two normal populations when the variances are unknown. If it is known that one specified variance is smaller than the other, then it is possible to modify the Graybill-Deal estimator in order to obtain a more efficient estimator. One such estimator is proposed by Mehta and Gurland (1969). We prove that this estimator is more efficient than the Graybill-Deal estimator under the condition that one variance is known to be less than the other.     

On the estimation of restricted mean

In sampling from a continuous distribution with unknown mean μ and variance σ² the problem of estimation of μ, when it is known that μ∈(a, ∞) (or μ∈(-∞, b)), is considered. The estimators proposed here lie in the interval (a, ∞) (or (-∞, b)) almost surely. The performance of these estimators is compared to that of some known estimators in the case of sampling from a normal, exponential and a weighted difference of two independent chi-square distributions.     

A note on the distribution of mean square error of forecasting

Simulation has been a very important and widely used method in the study of misspecification or order determination in time series analysis. Mean square error of forecasting (MSEF) has been a major criterion for comparing the performance of different models. In simulation studies, standard deviations of MSEF's are calculated from the computed values of the MSEF's, In this note, the distribution of MSEF from simulation studies is established. Exact variance of the MSEF can be obtained from the prespecified values of the model selected for simulation. This variance should be a more appropriate criterion for evaluating the performance between models.     

Constrained Bayes and empirical Bayes estimation under random effects normal ANOVA model with balanced loss function

The paper develops constrained Bayes and empirical Bayes estimators in the random effects ANOVA model under balanced loss functions. In the balanced normal–normal model, estimators of the Bayes risks of the constrained Bayes and constrained empirical Bayes estimators are provided which are correct asymptotically up to O(m^-1)$\mathrm{O}(m^{-1})$, that is the remainder term is o(m^-1)$\mathrm{o}(m^{-1})$, m$m$ denoting the number of strata.