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Diagnostic checking for multivariate regression models

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
99
Issue
9
Identifiers
DOI: 10.1016/j.jmva.2008.01.022
Keywords
  • 62H15
  • 62G09
  • 62G20
  • Multivariate Regression Model
  • Goodness-Of-Fit
  • Wilks Lambda
  • Score Tests
  • Nonparametric Monte Carlo Approximation
Disciplines
  • Mathematics

Abstract

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.

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