TY - JOUR
T1 - Diagnostic checking for multivariate regression models
AU - Zhu, Lixing
AU - Zhu, Ruoqing
AU - Song, Song
N1 - Funding Information:
The research was supported by a grant from the Research Grants Council of Hong Kong. The first author was in charge of the methodology and the second was in charge of the majority of the simulation results, and the third did part of the simulations. The authors thank the associate editor and referees for providing constructive comments and suggestions which led to an improvement of the presentation.
PY - 2008/10
Y1 - 2008/10
N2 - 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.
AB - 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.
KW - Multivariate regression model
KW - Goodness-of-fit
KW - Wilks lambda
KW - Score tests
KW - Nonparametric Monte Carlo approximation
UR - http://www.scopus.com/inward/record.url?scp=52749097198&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2008.01.022
DO - 10.1016/j.jmva.2008.01.022
M3 - Journal article
AN - SCOPUS:52749097198
SN - 0047-259X
VL - 99
SP - 1841
EP - 1859
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 9
ER -