Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions
نویسندگان
چکیده
Li & Racine (2008) consider the nonparametric estimation of conditional cumulative distribution functions (CDF) in the presence of discrete and continuous covariates along with the associated conditional quantile function. However, they did not propose an optimal data-driven method of bandwidth selection and left this important problem as an ‘open question’. In this paper we propose an automatic data-driven method for selecting these bandwidths, establish the asymptotic optimality of our approach, and derive asymptotic normality results for the resulting nonparametric estimator. By solving this ‘open question’ we thereby provide practitioners with an optimal nonparametric approach for estimating conditional CDF and quantile functions.
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