Stochastic comparisons of moment estimators of gamma distribution parameters

Piotr Nowak

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Displaying similar documents to “Stochastic comparisons of moment estimators of gamma distribution parameters”

Constructing median-unbiased estimators in one-parameter families of distributions via stochastic ordering

Ryszard Zieliński (2003)

Applicationes Mathematicae

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If θ ∈ Θ is an unknown real parameter of a given distribution, we are interested in constructing an exactly median-unbiased estimator θ̂ of θ, i.e. an estimator θ̂ such that a median Med(θ̂ ) of the estimator equals θ, uniformly over θ ∈ Θ. We shall consider the problem in the case of a fixed sample size n (nonasymptotic approach).

On non-existence of moment estimators of the GED power parameter

Bartosz Stawiarski (2016)

Discussiones Mathematicae Probability and Statistics

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We reconsider the problem of the power (also called shape) parameter estimation within symmetric, zero-mean, unit-variance one-parameter Generalized Error Distribution family. Focusing on moment estimators for the parameter in question, through extensive Monte Carlo simulations we analyze the probability of non-existence of moment estimators for small and moderate samples, depending on the shape parameter value and the sample size. We consider a nonparametric bootstrap approach and prove...

Gamma-minimax estimators for the parameters of a multinomial distribution

LanXiang Chen, J. Eichenauer-Herrmann, J. Lehn (1988)

Applicationes Mathematicae

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A note on stochastic ordering of estimators of exponential reliability

Piotr Nowak (2011)

Applicationes Mathematicae

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Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which the maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that the MLEs for those plans are also stochastically ordered. We also give some applications to the estimation of reliability.

Kernel estimators and the Dvoretzky-Kiefer-Wolfowitz inequality

Ryszard Zieliński (2007)

Applicationes Mathematicae

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It turns out that for standard kernel estimators no inequality like that of Dvoretzky-Kiefer-Wolfowitz can be constructed, and as a result it is impossible to answer the question of how many observations are needed to guarantee a prescribed level of accuracy of the estimator. A remedy is to adapt the bandwidth to the sample at hand.

Estimation of the parameters of Gumbel and Burr distributions in terms of kth record values

I. Malinowska, P. Pawlas, D. Szynal (2005)

Applicationes Mathematicae

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The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on m selected kth record values are presented for the parameters of the Gumbel and Burr distributions.

Comparison of six almost unbiased ratio estimators.

M. Dalabehera, L. N. Sahoo (1994)

Qüestiió

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In this paper, we compare six almost unbiased ratio estimators with respect to bias and efficiency for (i) finite populations, and (ii) infinite populations in which the joint distribution of the characters under study is bivariate normal.

Asymptotic normality and efficiency of variance components estimators with high breakdown points

Christine H. Müller (2000)

Discussiones Mathematicae Probability and Statistics

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For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared...

Estimating quantiles with Linex loss function. Applications to VaR estimation

Ryszard Zieliński (2005)

Applicationes Mathematicae

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Sometimes, e.g. in the context of estimating VaR (Value at Risk), underestimating a quantile is less desirable than overestimating it, which suggests measuring the error of estimation by an asymmetric loss function. As a loss function when estimating a parameter θ by an estimator T we take the well known Linex function exp{α(T-θ)} - α(T-θ) - 1. To estimate the quantile of order q ∈ (0,1) of a normal distribution N(μ,σ), we construct an optimal estimator in the class of all estimators...

Bayesian like R- and M- estimators of change points

Jaromír Antoch, Marie Husková (2000)

Discussiones Mathematicae Probability and Statistics

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The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.

Bayes unbiased estimators of parameters of linear trend with autoregressive errors

František Štulajter (1987)

Aplikace matematiky

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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. ...

An empirical evaluation of small area estimators.

Álex Costa, Albert Satorra, Eva Ventura (2003)

SORT

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This paper compares five small area estimators. We use Monte Carlo simulation in the context of both artificial and real populations. In addition to the direct and indirect estimators, we consider the optimal composite estimator with population weights, and two composite estimators with estimated weights: one that assumes homogeneity of within area variance and squared bias and one that uses area-specific estimates of variance and squared bias. In the study with real population, we found...

Robust estimators and their relations

J. Jurečková (1983)

Acta Universitatis Carolinae. Mathematica et Physica

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