Exact and asymptotic distributions of LULU smoothers |
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| Affiliation: | 1. Department of Statistics and Actuarial Science, University of Stellenbosch, Stellenbosch 7600, South Africa;2. Department of Quantitative Management, University of South Africa, Pretoria 0001, South Africa;1. Katholieke Universiteit LeuvenDepartment of Mathematics andUniversity Statistics Centrede Croylaan 543001 LeuvenBELGIUMK;2. Katholieke Universiteit LeuvenUniversity Statistics Centrede Croylaan 543001 LeuvenBELGIUM;3. Katholieke Universiteit LeuvenDepartment of Mathematics andUniversity Statistics Centrede Croylaan 543001 LeuvenBELGIUM;4. Katholieke Universiteit LeuvenDepartment of MathematicsCelestijnenlaan 200B3001 LeuvenBELGIUM;5. Center for Statistics Hasselt University Agoralaan - building D 3590 Diepenbeek BELGIUM |
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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. |
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