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    Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals

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    Date
    2016
    Author
    Janssen, Paul
    Swanepoel, Jan
    Veraverbeke, Noël
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    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
    URI
    http://hdl.handle.net/10394/21445
    https://doi.org/10.1007/s11749-015-0459-x
    https://link.springer.com/article/10.1007%2Fs11749-015-0459-x
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