Decision theoretic estimation using record statistics

Mohamed T. Madi

doi:10.1007/s00184-005-0009-8

Decision theoretic estimation using record statistics

Mohamed T. Madi

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We consider the problem of estimating the scale parameter θ of the shifted exponential distribution with unknown shift based on a set of observed records drawn from a sequential sample of independent and identically distributed random variables. Under a large class of bowl-shaped loss functions, the best affine equivariant estimator (BAEE) of θ is shown to be inadmissible. Two dominating procedures are proposed. A numerical study is performed to show the extent of risk reduction that the improved estimators provide over the BAEE.

Original language	English
Pages (from-to)	91-97
Number of pages	7
Journal	Metrika
Volume	63
Issue number	1
DOIs	https://doi.org/10.1007/s00184-005-0009-8
Publication status	Published - Mar 1 2006

Keywords

Entropy loss
Equivariant estimator
Exponential distribution
Improved estimation
Mean squared error
Record statistics
Risk reduction
Scale parameter

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00184-005-0009-8

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AB - We consider the problem of estimating the scale parameter θ of the shifted exponential distribution with unknown shift based on a set of observed records drawn from a sequential sample of independent and identically distributed random variables. Under a large class of bowl-shaped loss functions, the best affine equivariant estimator (BAEE) of θ is shown to be inadmissible. Two dominating procedures are proposed. A numerical study is performed to show the extent of risk reduction that the improved estimators provide over the BAEE.

KW - Entropy loss

KW - Equivariant estimator

KW - Exponential distribution

KW - Improved estimation

KW - Mean squared error

KW - Record statistics

KW - Risk reduction

KW - Scale parameter

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Decision theoretic estimation using record statistics

Abstract

Keywords

ASJC Scopus subject areas

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