Publication detail

# Statistical properties of the local linear estimator of conditional density

KONEČNÁ, K.

Original Title

Statistical properties of the local linear estimator of conditional density

English Title

Statistical properties of the local linear estimator of conditional density

Type

conference paper

Language

en

Original Abstract

This contribution focuses on the kernel conditional density estimations. % which provides a very comprehensive information about the analyzed data set. There are two basic estimators - the Nadaraya-Watson and the local linear estimator, we deal with the statistical properties of the second one. Derived characteristics of bias and variance of the estimator are compared with the results of the other authors via simulation study. The simulation study proved better statistical properties of the suggested characteristics. Additionally, the optimal values of smoothing parameters are derived by minimizing of Asymptotic Mean Integrated Squared Error. A data-driven method for practical estimation of the smoothing parameters is suggested - the derivation of formulas for the cross-validation method is extended from the Nadaraya-Watson to the local linear estimator.

English abstract

This contribution focuses on the kernel conditional density estimations. % which provides a very comprehensive information about the analyzed data set. There are two basic estimators - the Nadaraya-Watson and the local linear estimator, we deal with the statistical properties of the second one. Derived characteristics of bias and variance of the estimator are compared with the results of the other authors via simulation study. The simulation study proved better statistical properties of the suggested characteristics. Additionally, the optimal values of smoothing parameters are derived by minimizing of Asymptotic Mean Integrated Squared Error. A data-driven method for practical estimation of the smoothing parameters is suggested - the derivation of formulas for the cross-validation method is extended from the Nadaraya-Watson to the local linear estimator.

Keywords

kernel smoothing; conditional density; local linear estimator; statistical properties; bandwidths; cross-validation method

Released

15.06.2017

Location

Brno

ISBN

978-80-7231-417-1

Book

Matematika, informační technologie a aplikované vědy, MITAV 2017

Pages from

1

Pages to

7

Pages count

7

BibTex

``````
@inproceedings{BUT137455,
author="Kateřina {Pokorová}",
title="Statistical properties of the local linear estimator of conditional density",
annote="This contribution focuses on the kernel conditional density estimations. % which provides a very comprehensive information about the analyzed data set.
There are two basic estimators - the Nadaraya-Watson and the local linear estimator, we deal with the statistical properties of the second one. Derived characteristics of bias and variance of the estimator are compared with the results of the other authors via simulation study. The simulation study proved better statistical properties of the suggested characteristics.
Additionally, the optimal values of smoothing parameters are derived by minimizing of Asymptotic Mean Integrated Squared Error. A data-driven method for practical estimation of the smoothing parameters is suggested - the derivation of formulas for the cross-validation method is extended from the Nadaraya-Watson to the local linear estimator.
",
booktitle="Matematika, informační technologie a aplikované vědy, MITAV 2017",
chapter="137455",
howpublished="electronic, physical medium",
year="2017",
month="june",
pages="1--7",
type="conference paper"
}``````