Statistics Inference Of Partial Functional Linear Models Based On Rank Regression

Functional data analysis is a technique to process high-dimensional and dependent data.Based on the functional principal component analysis method,infinite-dimensional function objects can be approximated by finite-dimensional functional basis for regression analysis.Partially linear functional model is a type of model in functional data.It has received extensive attention from many scholars due to its high flexibility.However,most of the current research results are based on the least square and maximum likelihood method,and only a few articles consider robust estimation methods such as quantile regression.Real problem usually contains outliers.Estimation methods based on least square or likelihood functions are sensitive to outliers,and statistical inference results are unreliable in such a situation.Therefore,there is an urgent need to explore robust estimation method of partially linear function data.This dissertation studies partially functional linear model,considering the rank regression and variable selection issues.The main difficulty is that the model contains infinite-dimensional functional data and scalar data at the same time,and the objective function is a non-smooth function.The method used in this article is to first use the functional principal component analysis and truncated it according to cumulative variance contribution rate.The rank regression method is used to estimate the parameters of the truncated model,and adaptive LASSO is considered for variable selection.The asymptotic properties of parameter estimation are obtained through the asymptotic equivalent form of the objective function.Finally,numerical simulations verify the performance of the method in this dissertation under finite samples.