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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/21637

Title: Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals
Authors: Janssen, Paul
Swanepoel, Jan
Veraverbeke, Noël
Issue Date: 2016
Publisher: SPRINGER
Citation: TEST, 25 (2), p. 351-374
Abstract: Bernstein estimators attracted considerable attention as smooth nonparametric estimators for distribution functions, densities, copulas and copula densities. The present paper adds a parallel result for the first-order derivative of a copula function. This result then leads to Bernstein estimators for a conditional distribution function and its important functionals such as the regression and quantile functions. Results of independent interest have been derived such as an almost sure oscillation behavior of the empirical copula process and a Bahadur-type almost sure asymptotic representation for the Bernstein estimator of a regression quantile function. Simulations demonstrate the good performance of the proposed estimators.
Notes: [Janssen, Paul; Veraverbeke, Noel] Hasselt Univ, Ctr Stat, Hasselt, Belgium. [Swanepoel, Jan; Veraverbeke, Noel] North West Univ, Potchefstroom, South Africa.
URI: http://hdl.handle.net/1942/21637
DOI: 10.1007/s11749-015-0459-x
ISI #: 000375792600012
ISSN: 1133-0686
Category: A1
Type: Journal Contribution
Validation: ecoom, 2017
Appears in Collections: Research publications

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