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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. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, September.
    2. 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.
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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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