Variable Selection And Hypothesis Test For High Dimensional Nonparametric And Interactive Effects Model

The 21 st century is surely the century of data.Technological innovation has had a profound impact on social and scientific research,with financial markets,biomedicine,genomics,hyperspectral imagery,Internet portals and DNA microarrays generating a torrential stream of high dimensional data.Traditional statistical methods are difficult to deal with such data due to the high dimensional structure,where the dimension of covariates may even be much larger than the sample size.For high dimensional data,how to effectively carry out variable selection,statistical inference and implementation has been widely concerned by scholars.Its research results not only have important theoretical significance,but also have a wide range of application,and have become one of the international hot spots and frontier issues in the field of statistics.Interaction effect analysis can establish a broader statistical model and better understand the mechanism of covariates,which is of great practical significance to research and has attracted extensive attention.In addition,as a kind of generalized model,nonparametric transformation model includes many popular models as its special cases,so it is of great theoretical significance and practical value to study the variable selection and statistical inference for this model.The main research contents of this paper include the following three parts: Firstly,this paper studies the variable selection and parameter estimation under the highdimensional non-parametric transformation model,gives the non-asymptotic error bounds,and designs the efficient algorithm Group Fabs.Secondly,this paper proposes a general framework for the interaction identification of genomics data with hierarchical structure,designs the efficient algorithm Hier Fabs,and gives the theoretical properties of the algorithm.Finally,this paper considers test all regression parameters of nonparametric transformation model for high dimensional right censored data.Based on the partial rank loss function,we propose a partial rank score test and build the asymptotic distribution of the test statistic under the null hypothesis and local alternative hypothesis.