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Decision theoretic estimation using record statistics

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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.

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References

  • Ahsanullah M (1995) Introduction to record statistics. NOVA Science, Huntington New York USA

    Google Scholar 

  • Ahsanullah M, Nevzorov VB (2001) Ordered random variables. NOVA Science, Huntington New York USA

    MATH  Google Scholar 

  • Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York

    MATH  Google Scholar 

  • Brewster JF (1974) Alternative estimators for the scale parameter of the exponential distribution with unknown location. Ann Stat 2:553–557

    Article  MATH  MathSciNet  Google Scholar 

  • Brewster JF, Zidek JV (1974) Improving on equivariant estimators. Ann Stat 2:21–38

    Article  MATH  MathSciNet  Google Scholar 

  • Elfessi A (1997) Estimation of a linear function of the parameters of an exponential distribution from doubly censored samples. Stat Prob Lett 36:251–259

    Article  MATH  MathSciNet  Google Scholar 

  • Madi MT, Tsui KW (1990) Estimation of the ratio of the scale parameters of two exponential distributions with unknown location parameters. Ann Inst Stat Math 42:77–87

    Article  MATH  MathSciNet  Google Scholar 

  • Madi MT (1993) Alternative estimators for the variance of several normal distributions. Stat Proba Lett 17:321–328

    Article  MATH  MathSciNet  Google Scholar 

  • Madi MT (2002) On the invariant estimation of an exponential scale using doubly censored data. Stat Proba Lett 56:77–82

    Article  MATH  MathSciNet  Google Scholar 

  • Rukhin AL, Zidek JV (1985) Estimation of linear parametric functions for several exponential samples. Stat Decis 3:225–238

    MATH  MathSciNet  Google Scholar 

  • Zidek JV (1973) Estimating the scale parameter of the exponential distribution with unknown locations. Ann Stat 1:264–278

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, UAE University, Al Ain, United Arab Emirates

    Mohamed T. Madi

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  1. Mohamed T. Madi
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Correspondence to Mohamed T. Madi.

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Madi, M.T. Decision theoretic estimation using record statistics. Metrika 63, 91–97 (2006). https://doi.org/10.1007/s00184-005-0009-8

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  • DOI: https://doi.org/10.1007/s00184-005-0009-8

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