SEMIPARAMETRIC INFERENCE BY

Semi-parametric and nonparametric modeling and inference have been widely studied during the last two decades. In this manuscript, we do statistical inference based on semi-parametric and nonparametric models in several different scenarios. Firstly, we develop a semi-parametric additivity test for nonparametric multi-dimensional model. The test statistic can test two or higher way interactions and achieve the biggest local power when the interaction terms have Tukey’s format. Secondly, we develop a two step iterative estimating algorithm for generalized linear model with nonparametric varying dispersion. The algorithm is derived for heteroscedastic error generalized linear models, but it can be extended to 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 multivariate bioequivalence. 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 ∞ norm