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 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

Cite this

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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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JO - Metrika

JF - Metrika

IS - 1

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Decision theoretic estimation using record statistics

Abstract

Keywords

ASJC Scopus subject areas

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