Partial Linear Single-index Model For Quantile Regression Based On Integration Analysis

In recent years,the semi-parametric regression model has been gradually prevailing in the statistical method.Both the theoretical research and the practical application have attracted the attention of many scholars.Partial linear single-index model(PLSIM)is a very important high-dimensional semi-parametric model,which can effectively solve the problem of high-dimensional data,maintain good explanatory and wide adaptability.At present,the estimation methods of PLSIM model are mostly based on mean regression.However,when the data has abnormal values,random error is heteroscedasticity or deviates from normal distribution,the estimation accuracy of the model will be greatly reduced.In addition,domestic and foreign scholars' research on partial linear single-index model is more based on variable coefficient and local polynomial methods.When the variable dimension is higher and the data volume is large,the calculation speed of the model will become slow.Therefore,this paper studies the partial linear single-index model for quantile regression(QPLSIM)and its variable selection by combining the quantile regression and semi-parameter methods,adopts b-spline function approximation to the established model,introduces the MCP penalty function and proposes a two-stage estimation algorithm based on the iterative weighted least squares and simplex search method.Under certain conditions,this paper proves the asymptotic normality of model parameter estimation and oracle property of variable selection,and verifies the validity of the proposed method through numerical simulation and empirical analysis,which greatly improved the calculation speed of the model while ensuring the accuracy.In addition,data sets tend to have differences in source,format or subject,and present high dimensional and sparse characteristics.Based on multiple data sets,how to establish an appropriate statistical method to mine homogeneity and heterogeneity among different subsamples and achieve dimensional reduction and denoising is one of the major challenges faced by big data analysis.Integration analysis can consider multiple data sets at the same time to avoid model instability caused by time,region and other factors,which is an effective method to study data differences.It considers the coefficients of each covariate in all data sets as a group,introduces the penalty function to compress the coefficient group in two layers,studies the correlation between variables and realizes the dimensionality reduction.Therefore,based on the QPLSIM model,this paper continues to conduct in-depth research and proposes a partial linear single-index model for quantile regression based on the integration analysis(IAQPLSIM).Aiming at heterogeneous data,this paper adopts the composite penalty(Composite MCP)that considers both intra-group and inter-group variable selection at the same time,proves the oracle property of variable selection under certain conditions,and verifies the validity of the proposed method through numerical simulation and empirical analysis.Finally,the results of IAQPLSIM model and QPLSIM model were compared,and it was found that the estimation accuracy and variable selection accuracy of IAQPLSIM model were higher,and the fitting effect of the model was better.