Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information
1970 ◽
Vol 13
(3)
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pp. 391-393
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Keyword(s):
Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.
2003 ◽
Vol 54
(1-2)
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pp. 17-30
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1982 ◽
Vol 11
(8)
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pp. 941-955
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1997 ◽
Vol 47
(3-4)
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pp. 167-180
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2014 ◽
Vol 14
(07)
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pp. 1450026
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2005 ◽
Vol 14
(3)
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pp. 331-341
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Keyword(s):
2013 ◽
Vol 10
(2)
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pp. 480-488
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2018 ◽
pp. 439
2018 ◽
pp. 397