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"
}