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Diagnostic checking for multivariate regression models

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  • Zhu, Lixing
  • Zhu, Ruoqing
  • Song, Song

Abstract

Diagnostic checking for multivariate parametric models is investigated in this article. A nonparametric Monte Carlo Test (NMCT) procedure is proposed. This Monte Carlo approximation is easy to implement and can automatically make any test procedure scale-invariant even when the test statistic is not scale-invariant. With it we do not need plug-in estimation of the asymptotic covariance matrix that is used to normalize test statistic and then the power performance can be enhanced. The consistency of NMCT approximation is proved. For comparison, we also extend the score type test to one-dimensional cases. NMCT can also be applied to diverse problems such as a classical problem for which we test whether or not certain covariables in linear model has significant impact for response. Although the Wilks lambda, a likelihood ratio test, is a proven powerful test, NMCT outperforms it especially in non-normal cases. Simulations are carried out and an application to a real data set is illustrated.

Suggested Citation

  • Zhu, Lixing & Zhu, Ruoqing & Song, Song, 2008. "Diagnostic checking for multivariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1841-1859, October.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:1841-1859
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    References listed on IDEAS

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    1. Simonoff, Jeffrey S. & Tsai, Chih-Ling, 1991. "Assessing the influence of individual observations on a goodness-of-fit test based on nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 9-17, July.
    2. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    3. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    4. Winfried Stute & Li‐Xing Zhu, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545, September.
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