On the likelihood ratio test for envelope models in multivariate linear regression
Abbreviated Journal Title
Asymptotic null distribution; Envelope model; Likelihood ratio test; Multivariate linear regression; Partial envelope model; Saddlepoint; approximation; Biology; Mathematical & Computational Biology; Statistics & Probability
We investigate the likelihood ratio test for a hypothesis regarding the dimension of the Sigma-envelope of span(beta) in a multivariate linear regression model. The asymptotic null distribution of the likelihood ratio statistic is obtained as some nuisance parameters approach infinity. A saddlepoint approximation is also given for this limiting distribution. The accuracy of this approximation and its comparison to the standard chi-squared approximation are assessed via simulation. The results can be used in a similar test for partial envelope models.
"On the likelihood ratio test for envelope models in multivariate linear regression" (2013). Faculty Bibliography 2010s. 4657.