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Multiparameter estimation of discrete exponential distributions
Author(s) -
Tsui KamWah
Publication year - 1979
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315119
Subject(s) - estimator , mathematics , exponential family , exponential function , variance (accounting) , minimum variance unbiased estimator , statistics , distribution (mathematics) , random variable , natural exponential family , point (geometry) , exponential distribution , point estimation , mathematical analysis , geometry , accounting , business
Let X 1 , …, X p be independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of the p distributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained.