A note on the admissibility of hammersley's estimator of an integer mean | Zendy

Khan Rasul A. | Zendy

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A note on the admissibility of hammersley's estimator of an integer mean

Author(s) -

Khan Rasul A.

Publication year - 1978

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 - 10.2307/3314833

Subject(s) - mathematics , minimax , integer (computer science) , combinatorics , estimator , conjecture , independent and identically distributed random variables , zero (linguistics) , statistics , mean squared error , minimax estimator , class (philosophy) , maximum likelihood , random variable , discrete mathematics , minimum variance unbiased estimator , mathematical optimization , computer science , linguistics , philosophy , artificial intelligence , programming language

Let X 1 , X 2 , …, X n be identically, independently distributed N ( i ,1) random variables, where i = 0, ±1, ±2, … Hammersley (1950) showed that d = [X̄ n ], the nearest integer to the sample mean, is the maximum likelihood estimator of i . Khan (1973) showed that d is minimax and admissible with respect to zero‐one loss. This note now proves a conjecture of Stein to the effect that in the class of integer‐valued estimators d is minimax and admissible under squared‐error loss.

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