Estimation of the support of a discrete distribution

Nabendu Pal, Wei-Hsiung Shen and Bimal K. Sinha

Statistics & Probability Letters, 2000, vol. 48, issue 3, 287-292

Abstract: Let Y be a positive integer-valued random variable with the probability mass function P[theta](Y=y)=f(y;r)/a([theta]), y=r,r+1,...,[theta], where r is a known positive integer, and [theta][set membership, variant][Theta]={r,r+1,...} is an unknown parameter. We show that, for estimating [theta], cY is inadmissible under both 0-1 and a general loss whenever 0 1 in the case of sampling with replacement and discuss their bias and mean-squared error ([cY] denotes the integer nearest to cY).

Keywords: Admissible; Hammersley-Chapman-Robbins; inequality; Mean-squared; error; Minimax; Population; size; Squared; error; loss; 0-1; loss (search for similar items in EconPapers)
Date: 2000
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