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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, Noel |
Issue Date: | 2016 | Publisher: | SPRINGER | Source: | 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. | Keywords: | asymptotic normality; asymptotic representation; Bernstein estimation; copula; copula density; oscillation of empirical copula process; quantile function;Asymptotic normality; Asymptotic representation; Bernstein estimation; Copula; Copula density; Oscillation of empirical copula process; Quantile function | Document URI: | http://hdl.handle.net/1942/21637 | ISSN: | 1133-0686 | e-ISSN: | 1863-8260 | DOI: | 10.1007/s11749-015-0459-x | ISI #: | 000375792600012 | Rights: | © Sociedad de Estadística e Investigación Operativa 2015 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2017 |
Appears in Collections: | Research publications |
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