Extension Of Slice Inverse Regression Model And Its Application

With the development of computer technology,dealing with massive amount datais becoming increasingly popular,especially the data sets containing a large number ofvariables. How can we get the useful information of dimension reduction inlarge-scale data in the case of no information defected has become a major issue facedby statisticians. Sufficient dimension reduction is just the useful and important toolto deal with dimension reduction problems.Its basic idea is to make low dimensionprojection under the premise of no loss of information to achieve the purpose ofdimension.One of important theory of Sufficient dimension reduction is to estimate basicvectors of center dimension space to determine the basic direction.Sliced inverseregression is one of important methods to estimate the basic direction,which is basedon the first moment to identify center dimension space.However,there is a limitation.when the regression function is in symmetry,the method fails.The paper is mainly toextend sliced inverse regression to solve the inverse regression problem.When the regression function is in symmetry,two improved models areproposed.One is based on the sliced inverse regression,extending two-dimension ofarguments to estimate direction of multiple regression,and,use the direction to makeweights amendment of independent variables,then,solve the validity of the varianceestimation of first moment,at the same time,prove that the weights amendment couldeffectively estimate the center of reduced space.Another is based on the outer productof gradient to extend two-dimension of arguments to estimate direction of multipleregression,and,use the direction to make director estimation of gradient,then,solve thevalidity of the sliced inverse regression when the regression is symmetrical.Through simulation,in a simple regression,the two new proposed method are aswell as the other basic reduction methods.When the regression function is insymmetry,the new proposed methods could effectively reduce the dimension ofvariables.At last,make comparison of the new proposed methods and the basicreduction methods through using them in two sets examples,and get the validity of thenew methods.At the same time,get the actual process of model selection.When there isa strong correlation between the independent variables,several dimension reductionmethods are all good.In order to make things simple and interpretation factorssimplicity and conveniently,principle component analysis can be used.When there is little correlation between variables,sliced inverse regression and the new proposedmethods are considered.When the sliced inverse regression fails,use the new proposedmethods to reduce dimension.