Semiparametric Inference

Semi-parametric and nonparametric modeling and inference have been widely studied duringthe last two decades. In this manuscript, we do statistical inference based on semi-parametricand nonparametric models in several different scenarios.Firstly, we develop a semi-parametric additivity test for nonparametric multi-dimensionalmodel. The test statistic can test two or higher way interactions and achieve the biggest localpower when the interaction terms have Tukey's format. Secondly, we develop a two step iterativeestimating algorithm for generalized linear model with nonparametric varying dispersion. Thealgorithm is derived for heteroscedastic error generalized linear models, but it can be extendedto more general setting for example censored data.Thirdly, we develop a multivariate intersection-union bioequivalence test. The intersection-union test is uniform more powerful compare with other common used test for multivariatebioequivalence. Fourthly, we extend the multivariate bioequivalence test to functional data,which can also be considered as high dimensional multivariate data. We develop two bioequiv-alence test based on L2 and L infinity norm.We illustrate the issues and methodology by both simulation and in the context of ultrasoundsafety study, backscatter coefficient vs. frequency study as well as a pharmacokinetics study.