Diagnostic checking for multivariate regression models

Lixing Zhu*, Ruoqing Zhu, Song Song

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1841-1859
Number of pages19
JournalJournal of Multivariate Analysis
Issue number9
Publication statusPublished - Oct 2008

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Multivariate regression model
  • Goodness-of-fit
  • Wilks lambda
  • Score tests
  • Nonparametric Monte Carlo approximation


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