High Dimensional Stability And Multi-variable Selection Diagram Of The Model

With the rapid improvement of science and technology, this makes it possi-ble to mass and high dimension data today. How to dig out the useful information from the massive amount of data with relatively low cost is paid more and more attention, At the same time, the collected data must contain a large number of redundant information. Variable selection researches on how to choose the most important factors from the redundant variables. So variable selection is very important in statistical modeling. Traditional variable selection involves a combinatorial optimization problem, which is NP-hard, with computational time increasing exponentially with the dimensionality. The expensive compu-tational cost makes traditional procedures infeasible for high-dimensional data analysis. Meanwhile, the optimal subset method is not enough robust. So, in the high-dimensional case, we are looking for new variable selection methods to deal with it-the high dimension robust estimation and graphical models. In this paper, respectively on the basis of these two points, we propose the combined loss of LS,LAD in high-dimension and a group bridge approach for joint estima-tion of multiple graphical models. By studying the robust statistical properties of high-dimensional, the expressions of robust estimation are obtained, and we establish the asymptotic consistency and sparsistency of the proposed parameter estimation. The main results are presented as follows:In chapter1, we systematically introduces the background and development of variable selection and graphical models.In chapter2, we study the robust statistical properties and penalized robust statistical properties of high dimension. In these two parts, we first review the specific expression of the parameter estimation which is existed several kinds of loss function. Then by studying a convex combination of LS+LAD, the expres-sions of robust estimation and penalized robust estimation are obtained. The result reveals that the loss function model of convex combination combines the advantages of the LS and LAD, at the same time, it relatively weakens their shortcomings, thus it has excellent high dimensional statistical properties.In chapter3, combining with a single graphical model and l1penalized multiple graphical model, we propose a method that links the estimation of separate graphical models through a hierarchical penalty. By studying the high-dimensional statistical properties of the new model, we establish the asymptotic consistency and sparsistency of the proposed parameter estimation. The result reveals that it is capable of simultaneous selection at both the group and within-group individual variable levels.