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Bad luck in quadratic improvement of the linear estimator in a special linear model

Gejza Wimmer (1998)

Applications of Mathematics

The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.

Bayes and empirical bayes tests for the life parameter

Lichun Wang (2005)

Applicationes Mathematicae

We study the one-sided testing problem for the exponential distribution via the empirical Bayes (EB) approach. Under a weighted linear loss function, a Bayes test is established. Using the past samples, we construct an EB test and exhibit its optimal rate of convergence. When the past samples are not directly observable, we work out an EB test by using the deconvolution kernel method and obtain its asymptotic optimality.

Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior

Marek Męczarski, Ryszard Zieliński (1997)

Applicationes Mathematicae

A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.

Bayes robustness via the Kolmogorov metric

Agata Boratyńska, Ryszard Zieliński (1993)

Applicationes Mathematicae

An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.

Bayes sequential estimation procedures for exponential-type processes

Ryszard Magiera (1994)

Applicationes Mathematicae

The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.

Bayes unbiased estimation in a model with three variance components

Jaroslav Stuchlý (1989)

Aplikace matematiky

In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model 𝐭 = 𝐗 β + ϵ , 𝐄 ( 𝐭 ) = 𝐗 β , 𝐕𝐚𝐫 ( 𝐭 ) = 0 1 𝐔 1 + 0 2 𝐔 2 + 0 3 𝐔 3 , with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.

Bayes unbiased estimation in a model with two variance components

Jaroslav Stuchlý (1987)

Aplikace matematiky

In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model 𝐭 = 𝐗 β + ϵ , 𝐄 ( 𝐭 ) = 𝐗 β , 𝐃 ( 𝐭 ) = 0 1 𝐔 1 + 0 2 𝐔 2 with the unknown variance componets in the normal case. The matrices 𝐔 1 , 𝐔 2 may be singular. Applications to two examples of the analysis of variance are given.

Bayes unbiased estimators of parameters of linear trend with autoregressive errors

František Štulajter (1987)

Aplikace matematiky

The method of least wquares is usually used in a linear regression model 𝐘 = 𝐗 β + ϵ for estimating unknown parameters β . The case when ϵ is an autoregressive process of the first order and the matrix 𝐗 corresponds to a linear trend is studied and the Bayes approach is used for estimating the parameters β . Unbiased Bayes estimators are derived for the case of a small number of observations. These estimators are compared with the locally best unbiased ones and with the usual least squares estimators.

Bayesian analysis of structural change in a distributed Lag Model (Koyck Scheme)

Arvin Paul B. Sumobay, Arnulfo P. Supe (2014)

Discussiones Mathematicae Probability and Statistics

Structural change for the Koyck Distributed Lag Model is analyzed through the Bayesian approach. The posterior distribution of the break point is derived with the use of the normal-gamma prior density and the break point, ν, is estimated by the value that attains the Highest Posterior Probability (HPP). Simulation study is done using R. Given the parameter values ϕ = 0.2 and λ = 0.3, the full detection of the structural change when σ² = 1 is generally attained at ν + 1. The after...

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

Abd Ellah, A. H. (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.This paper is concerned with the problem of deriving Bayesian prediction bounds for the future observations (two-sample prediction) from the inverse Weibull distribution based on generalized order statistics (GOS). Study the two side interval Bayesian prediction, point prediction under symmetric and asymmetric loss functions and the maximum likelihood (ML) prediction using "plug-in" procedure for future observations from the inverse...

Bayesian estimation of AR(1) models with uniform innovations

Hocine Fellag, Karima Nouali (2005)

Discussiones Mathematicae Probability and Statistics

The first-order autoregressive model with uniform innovations is considered. In this paper, we propose a family of BAYES estimators based on a class of prior distributions. We obtain estimators of the parameter which perform better than the maximum likelihood estimator.

Bayesian estimation of mixtures with dynamic transitions and known component parameters

Ivan Nagy, Evgenia Suzdaleva, Miroslav Kárný (2011)

Kybernetika

Probabilistic mixtures provide flexible “universal” approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs “naturally” in one-pass mode. This is important in on-line applications and/or extensive databases. It even copes with dynamic nature of components forming the mixture. However, the quasi-Bayesian estimation relies on mixing via constant...

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