Single-index Expectile Model For High-dimensional Data

With the rapid development of computer science and technology,various data collection tools came into being,which leads to the frequent occurrence of high-dimensional data.The emergence of high-dimensional data and the "Curse of dimensionality" brought by it make the traditional statistics and data analysis methods unable to analyze high-dimensional data.Therefore,the study of high-dimensional data has become a hot issue in statistics.We must consider how to overcome the"dimension curse" and improve the accuracy of statistical inference.In other words,when we use the model to fit high-dimensional data,how to reduce the dimension of the data used.The single-index model can avoid the "curse of dimensionality" problem of high-dimensional data by means of dimensionality reduction,and is a very important nonparametric model.In order to solve the problem of single-index model parameter estimation under high-dimensional data,this thesis chooses to combine expectile model to estimate parameters and perform variable selection,that is,to study a single-index expectile model.Expectile model has many advantages.Newey and Powell（1987）proposed a class of estimators for classical linear regression models that allow for the use of different weights for positive and negative residuals and called expected quantile regression.We choose asymmetric least squares（ALS）and Adaptive LASSO for parameter estimation and variable selection.This thesis introduces a new penalized ALS（PALS）method for efficient estimation of indicator coefficients in single-index expectile model with simultaneous variable selection.Combining the bias correction method with PALS,it can be proved that the proposed estimate has asymptotic normality,which can be used to construct effective confidence intervals and test hypotheses.