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Nonparametric estimation of location and scale parameters

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  • Potgieter, C.J.
  • Lombard, F.

Abstract

Two random variables X and Y belong to the same location-scale family if there are constants μ and σ such that Y and μ+σX have the same distribution. In this paper we consider non-parametric estimation of the parameters μ and σ under minimal assumptions regarding the form of the distribution functions of X and Y. We discuss an approach to the estimation problem that is based on asymptotic likelihood considerations. Our results enable us to provide a methodology that can be implemented easily and which yields estimators that are often near optimal when compared to fully parametric methods. We evaluate the performance of the estimators in a series of Monte Carlo simulations.

Suggested Citation

  • Potgieter, C.J. & Lombard, F., 2012. "Nonparametric estimation of location and scale parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4327-4337.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4327-4337
    DOI: 10.1016/j.csda.2012.03.021
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    References listed on IDEAS

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    1. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
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    Cited by:

    1. Bhattacharya, Rianka & Subramanian, Sundarraman, 2014. "Two-sample location–scale estimation from semiparametric random censorship models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 25-38.

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