Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed to indicate quality of representation of interrelations among attributes in a battery by a maximum likelihood factor analysis. Usually, for a large sample of indiv...

We consider methods proposed for detecting localized spatial clustering. We propose a new test statistic, the weighted average likelihood ratio test, as an alternative to the spatial scan (maximum likelihood ratio) test statistic. Two different types of weights are considered. We propose an unbiased cluster selection criterion and evaluate the bias of the tests through simulation. We also exami...

In this paper we give a proof of the Wilks theorem for the empirical likelihood ratio test for the right censored data, when the hypothesis are formulated in terms of p estimating equations or mean functions. In particular we show that the empirical likelihood ratio test statistic is equal to a quadratic form similar to a Hotelling’s T 2 statistic, plus a small error. The least favorable distri...

For the analysis of an r by c contingency table having ordered row categories and ordered column categories, a bootstrap method is applied for the model-based likelihood ratio test for independence. A model-based likelihood ratio chi-square statistic and the statistic of the maximum eigenvalue of a Wishart matrix are also discussed. A simulation study is performed to compare the proposed method...

ii c 2013 Yi Liu ALL RIGHTS RESERVED iii ABSTRACT YI LIU. Generalized Quasi-Likelihood Ratio Statistics for Multivariate Time-varying Coefficient Regression Models. (Under the direction of DR. JIANCHENG JIANG) Generalized likelihood ratio statistics have been a generally applicable method for testing nonparametric hypotheses about nonparametric functions.It has been widely used in many research...

BACKGROUND New markers hold the promise of improving risk prediction for individual patients. We aimed to compare the performance of different strategies to extend a previously developed prediction model with a new marker. METHODS Our motivating example was the extension of a risk calculator for prostate cancer with a new marker that was available in a relatively small dataset. Performance of...