High-dimensional statistics for complex data

Abstract

High dimensional data analysis has become a popular research topic in the recent years, due to the emergence of various new applications in several fields of sciences underscoring the need for analysing massive data sets. One of the main challenge in analysing high dimensional data regards the interpretability of estimated models as well as the computational efficiency of procedures adopted. Such a purpose can be achieved through the identification of relevant variables that really affect the phenomenon of interest, so that effective models can be subsequently constructed and applied to solve practical problems. The first two chapters of the thesis are devoted in studying high dimensional statistics for variable selection. We firstly introduce a short but exhaustive review on the main developed techniques for the general problem of variable selection using nonparametric statistics. Lastly in chapter 3 we will present our proposal regarding a feature screening approach for non additive models developed by using of conditional information in the estimation procedure... [edited by Author]