Informatics and Applications
2015, Volume 9, Issue 3, pp 72-84
HIGHER-ORDER ASYMPTOTIC EXPANSIONS OF UNBIASED ESTIMATORS AND THEIR VARIANCES ON THE ONE-PARAMETER EXPONENTIAL FAMILY MODEL
Abstract
The paper considers a model of duplicate sampling with the fixed size n from a distribution belonging to the natural one-parameter exponential family A limiting behavior of the uniformly minimum variance unbiased estimator (UMVUE) of the given parametric function and the UMVUE variance of this estimator is studied in the case of infinite size of the sample. Higher-order asymptotic expansions are obtained for functions defining unbiased estimators and variances of these estimators. The results are presented for both the canonical parameterization and the mean parameterization.
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[+] About this article
Title
HIGHER-ORDER ASYMPTOTIC EXPANSIONS OF UNBIASED ESTIMATORS AND THEIR VARIANCES ON THE ONE-PARAMETER EXPONENTIAL FAMILY MODEL
Journal
Informatics and Applications
2015, Volume 9, Issue 3, pp 72-84
Cover Date
2015-02-30
DOI
10.14357/19922264150308
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
natural exponential family; unbiased estimate; asymptotic expansion
Authors
V. V. Chichagov 
Author Affiliations
Perm State University, 15 Bukireva Str., Perm 614990, Russian Federation
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