Exact and asymptotic distributions of LULU smoothers

Authors:
W. J. Conradie;T. de Wet;M. Jankowitz
Affiliations:
Department of Statistics and Actuarial Science, University of Stellenbosch, Stellenbosch 7600, South Africa;Department of Statistics and Actuarial Science, University of Stellenbosch, Stellenbosch 7600, South Africa;Department of Quantitative Management, University of South Africa, Pretoria 0001, South Africa
Venue:
Journal of Computational and Applied Mathematics - Special issue: Jef Teugels
Year:
2006

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Abstract

This paper considers a class of non-linear smoothers, called LULU smoothers, introduced by Rohwer in the late eighties in the mathematics literature, and since then investigated fairly extensively by a number of authors for its mathematical properties. They have been successfully applied in various engineering and scientific problems. However, to date their distribution theory has not received any attention in the literature. In this paper we derive their exact as well as asymptotic distributions and show their relationship to the upper order statistics.