Selection Of Variables For A Generalized Single Index Model Based On Empirical Likelihood

As an important semi-parametric model,generalized single-index model is often used to deal with multiple non-parametric regression problems,which has better applicability to complex data and high-dimensional data processing.Variable selection is an important problem in statistical modeling and one of the hot issues in statistical research.In regression modeling,when covariates have sparsity,it is particularly important to select variables.Although there are many literature studies on parameter estimation and confidence interval problems of single index models,there are few studies on variable selection problems of generalized single index models.Therefore,it is of great theoretical significance and use value to study the variable selection problem of generalized single index variable model.This paper mainly studies the variable selection problem of generalized single index model.Based on the merits of the empirical likelihood method,we will use the penalty contour empirical likelihood method to select variables for the generalized single index model.The first chapter mainly introduces the research background and significance of the generalized single index model and its variable selection problem,the chapter structure and innovation points of this paper.The second chapter gives the relevant background knowledge of this research,mainly discusses the Oracle properties of generalized single index model,empirical likelihood method,estimation equation,existing variable selection method and variable selection method.In the third chapter,we mainly discuss the variable selection problem of generalized single index regression model.first,by introducing an auxiliary vector,we give the estimation equation that the model parameters satisfy;secondly,we construct the contour empiricallikelihood based on the established estimation equation;thirdly,we select the SCAD function with good theoretical properties in the penalty function,and combine the selected contour empirical likelihood to construct the objective function of variable selection.BIC criteria are used to determine the selection of adjustment parameters in the penalty function to obtain our variable selection.proved the excellence of our variable selection method,that is,Oracle.The fourth chapters,we extend the method of the third chapter to the general case of generalized single-indicator model variable selection based on empirical likelihood method of generalized single index model,and prove its Oracle.In the fifth chapter,the proposed method is simulated numerically.the simulation results confirm that our variable selection method is very practical and excellent.