Displaying similar documents to “On the convergence of Bhattacharyya bounds in the multiparameter case”

On the convergence of the Bhattacharyya bounds in the multiparametric case

Abdulghani Alharbi (1994)

Applicationes Mathematicae

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Shanbhag (1972, 1979) showed that the diagonality of the Bhattacharyya matrix characterizes the set of normal, Poisson, binomial, negative binomial, gamma or Meixner hypergeometric distributions. In this note, using Shanbhag's techniques, we show that if a certain generalized version of the Bhattacharyya matrix is diagonal, then the bivariate distribution is either normal, Poisson, binomial, negative binomial, gamma or Meixner hypergeometric. Bartoszewicz (1980) extended the result of...

A Cramer-Rao analogue for median-unbiased estimators.

N. K. Sung, Gabriela Stangenhaus, Herbert T. David (1990)

Trabajos de Estadística

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Adopting a measure of dispersion proposed by Alamo [1964], and extending the analysis in Stangenhaus [1977] and Stangenhaus and David [1978b], an analogue of the classical Cramér-Rao lower bound for median-unbiased estimators is developed for absolutely continuous distributions with a single parameter, in which mean-unbiasedness, the Fisher information, and the variance are replaced by median-unbiasedness, the first absolute moment of the sample score, and the reciprocal of twice the...

Unbiased estimation for two-parameter exponential distribution under time censored sampling

S. Sengupta (2009)

Applicationes Mathematicae

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The problem considered is that of unbiased estimation for a two-parameter exponential distribution under time censored sampling. We obtain a necessary form of an unbiasedly estimable parametric function and prove that there does not exist any unbiased estimator of the parameters and the mean of the distribution. For reliability estimation at a specified time point, we give a necessary and sufficient condition for the existence of an unbiased estimator and suggest an unbiased estimator...

Unbiased estimation of reliability for two-parameter exponential distribution under time censored sampling

S. Sengupta (2010)

Applicationes Mathematicae

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The problem considered is that of unbiased estimation of reliability for a two-parameter exponential distribution under time censored sampling. We give necessary and sufficient conditions for the existence of uniformly minimum variance unbiased estimator and also provide a characterization of a complete class of unbiased estimators in situations where unbiased estimators exist.

On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.

Jadwiga Kicinska-Slaby (1982)

Trabajos de Estadística e Investigación Operativa

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Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ-r of unknown parameter λ of gamma distribution with density f(x|λ, b) = λb-1 e-λx xb-1 / Γ(b), x>0, where b is a known parameter, for loss function L(λ -r, λ-r...

Estimation of a quadratic function of the parameter of the mean in a linear model

Júlia Volaufová, Peter Volauf (1989)

Aplikace matematiky

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The paper deals with an optimal estimation of the quadratic function β ' 𝐃 β , where β ∈ ℛ k , 𝐃 is a known k × k matrix, in the model 𝐘 , 𝐗 β , σ 2 𝐈 . The distribution of 𝐘 is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix 𝐗 .

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).

Estimation of intersection intensity in a Poisson process of segments

Tomáš Mrkvička (2007)

Commentationes Mathematicae Universitatis Carolinae

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The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.