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Local Power Properties of Kernel Based Goodness of Fit Tests

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  • Gouriéroux, Christian
  • Tenreiro, Carlos

Abstract

If (Xi, i[set membership, variant]) 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).

Suggested Citation

  • Gouriéroux, Christian & Tenreiro, Carlos, 2001. "Local Power Properties of Kernel Based Goodness of Fit Tests," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 161-190, August.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:2:p:161-190
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    References listed on IDEAS

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    1. repec:adr:anecst:y:1996:i:43:p:06 is not listed on IDEAS
    2. Fan, Yanqin, 1997. "Goodness-of-Fit Tests for a Multivariate Distribution by the Empirical Characteristic Function," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 36-63, July.
    3. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    4. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    5. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
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    1. Taoufik Bouezmarni & Jeroen V.K. Rombouts & Abderrahim Taamouti, 2011. "Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 275-287, October.
    2. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    3. Bagkavos, Dimitrios & Patil, Prakash N. & Wood, Andrew T.A., 2023. "Nonparametric goodness-of-fit testing for a continuous multivariate parametric model," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    5. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    6. Carlos Tenreiro, 2022. "On automatic kernel density estimate-based tests for goodness-of-fit," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 717-748, September.

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