Geodesic
Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information
Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 391-393

Voir la notice de l'article provenant de la source Cambridge

DOI

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. 
Kale, B. K. Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information. Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 391-393. doi: 10.4153/CMB-1970-076-x
@article{10_4153_CMB_1970_076_x,
     author = {Kale, B. K.},
     title = {Inadmissibility of the {Maximum} {Likelihood} {Estimator} in the {Presence} of {Prior} {Information}},
     journal = {Canadian mathematical bulletin},
     pages = {391--393},
     year = {1970},
     volume = {13},
     number = {3},
     doi = {10.4153/CMB-1970-076-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-076-x/}
}
TY  - JOUR
AU  - Kale, B. K.
TI  - Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information
JO  - Canadian mathematical bulletin
PY  - 1970
SP  - 391
EP  - 393
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-076-x/
DO  - 10.4153/CMB-1970-076-x
ID  - 10_4153_CMB_1970_076_x
ER  - 
%0 Journal Article
%A Kale, B. K.
%T Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information
%J Canadian mathematical bulletin
%D 1970
%P 391-393
%V 13
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-076-x/
%R 10.4153/CMB-1970-076-x
%F 10_4153_CMB_1970_076_x

Cité par Sources :