KAUST Grant NumberKUS-C1-016-04
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AbstractTwo 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. © 2012 Elsevier B.V. All rights reserved.
CitationPotgieter CJ, Lombard F (2012) Nonparametric estimation of location and scale parameters. Computational Statistics & Data Analysis 56: 4327–4337. Available: http://dx.doi.org/10.1016/j.csda.2012.03.021.
SponsorsThe first author's work was supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The second author's work was supported by the National Research Foundation of South Africa. The authors thank two referees for comments that led to an improved exposition of the work.