Uniform strong consistency of a frontier estimator using kernel regression on high order moments. (15th October 2014)

• Record Type: Journal Article
• Authors: Girard, Stéphane; Guillou, Armelle; Stupfler, Gilles
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 642
• Page End: 666
• Publication Date: 2014-10-15
• Subjects: Frontier estimation, -- kernel estimation, -- strong uniform consistency, -- Hall class; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013050
• Languages: English
• ISSNs: 1292-8100

Abstract

Abstract : We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, J. Multivariate Anal. 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.