Publication detail
The Priestley-Chao Estimator of Conditional Density with Uniformly Distributed Random Design
KONEČNÁ, K.
Original Title
The Priestley-Chao Estimator of Conditional Density with Uniformly Distributed Random Design
English Title
The Priestley-Chao Estimator of Conditional Density with Uniformly Distributed Random Design
Type
journal article in Web of Science
Language
en
Original Abstract
The present paper is focused on non-parametric estimation of conditional density. Conditional density can be regarded as a generalization of regression thus the kernel estimator of conditional density can be derived from the kernel estimator of the regression function. We concentrate on the Priestley-Chao estimator of conditional density with a random design presented by a uniformly distributed unconditional variable. The statistical properties of such an estimator are given. As the smoothing parameters have the most significant influence on the quality of the final estimate, the leave-one-out maximum likelihood method is proposed for their detection. Its performance is compared with the cross-validation method and with two alternatives of the reference rule method. The theoretical part is complemented by a simulation study.
English abstract
The present paper is focused on non-parametric estimation of conditional density. Conditional density can be regarded as a generalization of regression thus the kernel estimator of conditional density can be derived from the kernel estimator of the regression function. We concentrate on the Priestley-Chao estimator of conditional density with a random design presented by a uniformly distributed unconditional variable. The statistical properties of such an estimator are given. As the smoothing parameters have the most significant influence on the quality of the final estimate, the leave-one-out maximum likelihood method is proposed for their detection. Its performance is compared with the cross-validation method and with two alternatives of the reference rule method. The theoretical part is complemented by a simulation study.
Keywords
Priestley-Chao estimator of conditional density, random design, uniform marginal density, bandwidth selection, maximum likelihood method, reference rule method
Released
21.09.2018
Publisher
Český statistický úřad
Location
Česká republika
ISBN
0322-788X
Periodical
Statistika
Year of study
98
Number
3
State
CZ
Pages from
283
Pages to
294
Pages count
307
URL
Full text in the Digital Library
Documents
BibTex
@article{BUT150775,
author="Kateřina {Pokorová}",
title="The Priestley-Chao Estimator of Conditional Density with Uniformly Distributed Random Design",
annote="The present paper is focused on non-parametric estimation of conditional density. Conditional density can
be regarded as a generalization of regression thus the kernel estimator of conditional density can be derived
from the kernel estimator of the regression function. We concentrate on the Priestley-Chao estimator of
conditional density with a random design presented by a uniformly distributed unconditional variable. The
statistical properties of such an estimator are given. As the smoothing parameters have the most significant
influence on the quality of the final estimate, the leave-one-out maximum likelihood method is proposed for
their detection. Its performance is compared with the cross-validation method and with two alternatives of
the reference rule method. The theoretical part is complemented by a simulation study.",
address="Český statistický úřad",
chapter="150775",
howpublished="print",
institution="Český statistický úřad",
number="3",
volume="98",
year="2018",
month="september",
pages="283--294",
publisher="Český statistický úřad",
type="journal article in Web of Science"
}