Variable Screening Based On Spearman Correlation

With the development for the science and technology, high-dimensional data has been widely used in the field of science research, such as genetics, finance, image processing etc. Because high-dimensional data can not be handled effectively by the current models or approaches,we need to make dimension reduction for high-dimensional data to make use of the available models and approaches now. The dissertation mainly contains the following two aspects:First, we point out that the traditional variable selection methods can not handle highdimensional data and give a unified form of traditional variable selection methods. Second, we introduce detailedly two variable screening methods: SIS(sure independent screening) method and RRCS(robust rank correlation screening) method. Last, we introduce the research status of other variable screening.Second, we make comparison and conclusion for the three popular correlation coefficient and puts forward a variable selection approach base on the Spearman correlation, which is a effective supplementary and perfection for SIS based on Pearson correlation and RRCS based on Kendall τ correlation.Variable screening based on Spearman correlation has three strong points in comparison to the SIS:(1) Sure screening property can be proved under a weaker condition;(2) Expect for the linear model, Spearman variable screening method can conduct others models with variable screening(eg. transformation model);(3) Using indicator function, U-statistic and the Copula theory in this paper has greatly simplified the proof process.Numerical simulation studies will be presented in chapter 3. At the end of the paper, we give the conclusion for the Spearman variable screening, and summarize the primary research achievements, and ultimately point out the further researching topic and direction.