Publication details

Priestley-Chao Estimator of Conditional Density


KONEČNÁ Kateřina

Year of publication 2017
Type Article in Proceedings
Conference Mathematics, Information Technologies and Applied Sciences 2017, post-conference proceedings of extended versions of selected papers
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords kernel smoothing; conditional density; Priestley-Chao estimator; statistical properties; bandwidth selection; cross-validation method
Description This contribution is focused on a non-parametric estimation of conditional density. Several types of kernel estimators of conditional density are known, the Nadaraya-Watson and the local linear estimators are the widest used ones. We focus on a new estimator - the Priestley-Chao estimator of conditional density. As conditional density can be regarded as a generalization of regression, the Priestley-Chao estimator, proposed initially for kernel regression, is extended for kernel estimation of conditional density. The conditional characteristics and the statistical properties of the suggested estimator are derived. The estimator depends on the smoothing parameters called bandwidths which influence the final quality of the estimate significantly. The cross-validation method is suggested for their estimation and the expression for the cross-validation function is derived.
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