Estimation in uniform distributions using orthogonal polynomials

The purpose of this paper is to study some problems of parametric estimation in the U(0,θ) distribution. Using expansions in terms of orthogonal polynomials, we compare the asymptotic behaviour of the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) fo...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 28; no. 5; pp. 1145 - 1167
Main Authors Barranco-Chamorro, T., Lopez-Blazquez, F., Moreno-Rebollo, J.L.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Marcel Dekker, Inc 01.01.1999
Taylor & Francis
Subjects
asymptotic properties
Distribution theory
Exact sciences and technology
Linear inference, regression
Mathematics
maximum likelihood estimation
minimum variance estimation
nonregular distributions
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
Parameter estimation
Uniform distribution
Unbiased estimation
Asymptotic behavior
Distribution function
Maximum likelihood
Variance analysis
Orthogonal polynomial
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Summary:The purpose of this paper is to study some problems of parametric estimation in the U(0,θ) distribution. Using expansions in terms of orthogonal polynomials, we compare the asymptotic behaviour of the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) for a given one-parameter estimable function. We also give conditions under which the results obtained can be extended to certain distributions whose range depends on an unknown parameter.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610929908832349