| Sufficient dimension reduction and variable selection has been an important research area in statistics.Traditional variable selection method is not suitable for high dimensional data which is produced due to the development of science and technology.Meanwhile,there is group information between variables.So statistician have concerned about that how to integrate the structured information into the variable selection.In this thesis,we first introduce the sliced inverse regression(SIR),which is used to process high dimensional data,and its improved methods,the random sliced inverse regression(r SIR)as well as group sufficient dimension reduction(g SDR).Then,we develop a novel method called random group sliced inverse regression(rg SIR).This method combines the random sliced inverse regression with the group sufficient dimension reduction.The rg SIR can not only make use of the group information of the original data,but also can be applied to the high dimensional data which the number of variables is much larger than the number of samples.It solves the drawbacks that r SIR ignors group information and g SDR cannot be applied to high dimensional data.We simulate the data sets in the condition of different group information and different structural dimension.The simulation results show that the rg SIR algorithm performs better both in high and low dimensional data.In the actual data analysis,we first perform variable selection with rg SIR based on the training set,build a classification rule with the linear discriminant analysis,and then apply this rule to the testing set.The result indicates that rg SIR has less predictor error than other sparse sufficient dimension reduction. |
