A nonparametric test of fit of a parametric model

Andrzej S. Kozek

doi:10.1016/0047-259X(91)90111-E

A nonparametric test of fit of a parametric model

Andrzej S. Kozek^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We propose a natural test of fit of a parametric regression model. The test is based on a comparison of a nonparametric kernel estimate of a regression function with its least-squares parametric estimate. Under the null hypothesis we derive approximations to the probability distribution functions of the test statistic. The approximations are exact with a power rate. Moreover, we prove the consistency of the test.

Original language	English
Pages (from-to)	66-75
Number of pages	10
Journal	Journal of Multivariate Analysis
Volume	37
Issue number	1
DOIs	https://doi.org/10.1016/0047-259X(91)90111-E
Publication status	Published - 1991
Externally published	Yes

Keywords

least squares method
maximum deviation distribution
nonlinear regression
nonparametric regression
parametric regression
test of fit

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10.1016/0047-259X(91)90111-E

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abstract = "We propose a natural test of fit of a parametric regression model. The test is based on a comparison of a nonparametric kernel estimate of a regression function with its least-squares parametric estimate. Under the null hypothesis we derive approximations to the probability distribution functions of the test statistic. The approximations are exact with a power rate. Moreover, we prove the consistency of the test.",

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AB - We propose a natural test of fit of a parametric regression model. The test is based on a comparison of a nonparametric kernel estimate of a regression function with its least-squares parametric estimate. Under the null hypothesis we derive approximations to the probability distribution functions of the test statistic. The approximations are exact with a power rate. Moreover, we prove the consistency of the test.

KW - least squares method

KW - maximum deviation distribution

KW - nonlinear regression

KW - nonparametric regression

KW - parametric regression

KW - test of fit

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 1

ER -

A nonparametric test of fit of a parametric model

Abstract

Keywords

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