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Estimating a function of scale parameter of an exponential population with unknown location under general loss function

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  • Lakshmi Kanta Patra

    (Indian Institute of Petroleum and Energy)

  • Suchandan Kayal

    (National Institute of Technology Rourkela)

  • Somesh Kumar

    (Indian Institute of Technology Kharagpur)

Abstract

In the present study, we consider the problem of estimating a function of scale parameter $$\ln \sigma $$ ln σ under an arbitrary location invariant bowl-shaped loss function, when location parameter $$\mu $$ μ is unknown. Various improved estimators are proposed. Inadmissibility of the best affine equivariant estimator (BAEE) of $$\ln \sigma $$ ln σ is established by deriving a Stein-type estimator. This improved estimator is not smooth. We derive a smooth estimator improving upon the BAEE. Further, the integral expression of risk difference (IERD) approach of Kubokawa is used to derive a class of improved estimators. To illustrate these results, we consider two specific loss functions: squared error and linex loss functions, and derive various estimators improving upon the BAEE. Finally, a simulation study has been carried out to numerically compare the risk performance of the improved estimators.

Suggested Citation

  • Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2020. "Estimating a function of scale parameter of an exponential population with unknown location under general loss function," Statistical Papers, Springer, vol. 61(6), pages 2511-2527, December.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1052-7
    DOI: 10.1007/s00362-018-1052-7
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    References listed on IDEAS

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