Informatics and Applications
2016, Volume 10, Issue 3, pp 66-76
ASYMPTOTIC EXPANSIONS OF MEAN ABSOLUTE ERROR OF UNIFORMLY MINIMUM VARIANCE UNBIASED AND MAXIMUM LIKELIHOOD ESTIMATORS ON THE ONE-PARAMETER EXPONENTIAL FAMILY MODEL OF LATTICE DISTRIBUTIONS
Abstract
The paper considers a model of duplicate sampling with the fixed size n from a lattice distribution belonging to the natural one-parameter exponential family Asymptotic expansions of the mean absolute errors of the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) of the given parametric function are obtained in the case of infinite size of the sample. The case when G'[a] = 0 and G" [a] = 0 was studied separately. The relative error in calculating the difference in the mean absolute error UMVUE and MLE was evaluated in the case of the Poisson distribution for the two parametric functions. This error was received via the asymptotic expansions. It was found that the asymptotic results with a sufficiently large sample size allows one to compare UMVUE and MLE using such indicator of quality assessment as the mean absolute error.
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[+] About this article
Title
ASYMPTOTIC EXPANSIONS OF MEAN ABSOLUTE ERROR OF UNIFORMLY MINIMUM VARIANCE UNBIASED AND MAXIMUM LIKELIHOOD ESTIMATORS ON THE ONE-PARAMETER EXPONENTIAL FAMILY MODEL OF LATTICE DISTRIBUTIONS
Journal
Informatics and Applications
2016, Volume 10, Issue 3, pp 66-76
Cover Date
2016-08-30
DOI
10.14357/19922264160309
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
exponential family; lattice distribution; unbiased estimator; maximum likelihood estimator; asymptotic expansion
Authors
V. V. Chichagov 
Author Affiliations
Perm State University, 15 Bukireva Str., Perm 614990, Russian Federation
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