Journal
TEST
Volume 25, Issue 2, Pages 351-374Publisher
SPRINGER
DOI: 10.1007/s11749-015-0459-x
Keywords
Asymptotic normality; Asymptotic representation; Bernstein estimation; Copula; Copula density; Oscillation of empirical copula process; Quantile function
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Funding
- IAP Research Network of the Belgian State (Belgian Science Policy) [P7/13]
- National Research Foundation of South Africa
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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.
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