Local power properties of kernel based goodness of fit tests

Christian Gouriéroux; Carlos Tenreiro

doi:10.1006/jmva.2000.1950

Local power properties of kernel based goodness of fit tests

Christian Gouriéroux
, Carlos Tenreiro

CEPREMAP Centre pour la Recherche Économique et ses Applications
University of Coimbra

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

17 Citations (Scopus)

Abstract

If (X_i, i∈Z) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H0:{f=f0}, where f0 is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between f_n, a kernel estimator of f, and f₀, or between f_n and its expected value computed under H₀. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071-1095).

Original language	English
Pages (from-to)	161-190
Number of pages	30
Journal	Journal of Multivariate Analysis
Volume	78
Issue number	2
DOIs	https://doi.org/10.1006/jmva.2000.1950
Publication status	Published - 1 Aug 2001
Externally published	Yes

Keywords

Goodness of fit tests
asymptotic power
integrated square error
kernel density estimator
local alternatives

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10.1006/jmva.2000.1950

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abstract = "If (Xi, i∈Z) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H0:\{f=f0\}, where f0 is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between fn, a kernel estimator of f, and f0, or between fn and its expected value computed under H0. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071-1095).",

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AB - If (Xi, i∈Z) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H0:{f=f0}, where f0 is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between fn, a kernel estimator of f, and f0, or between fn and its expected value computed under H0. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071-1095).

KW - Goodness of fit tests

KW - asymptotic power

KW - integrated square error

KW - kernel density estimator

KW - local alternatives

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DO - 10.1006/jmva.2000.1950

M3 - Article

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SN - 0047-259X

VL - 78

SP - 161

EP - 190

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 2

ER -

Local power properties of kernel based goodness of fit tests

Abstract

Keywords

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