Sieve M-estimator for a semi-functional linear model  

作　　者：HUANG LeLe WANG HuiWen CUI HengJian WANG SiYang 

机构地区：[1]School of Economics and Management,Beihang University [2]School of Mathematical Sciences,Capital Normal University [3]School of Statistics and Mathematics,Central University of Finance and Economics

出　　处：《Science China Mathematics》2015年第11期2421-2434,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.71420107025,11071022,11231010 and 11471223);the Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D.graduates(Grant No.YWF-14-YJSY-027);the National High Technology Research and Development Program of China(863 Program)(Grant No.SS2014AA012303);Beijing Center for Mathematics and Information Interdisciplinary Sciences,Key Project of Beijing Municipal Educational Commission(Grant No.KZ201410028030);Youth Doctor Development Funding Project for"121"Human Resources of Central University of Finance and Economics(Grant No.QBJ1423)

摘　　要：We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method.We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables. Spline estimators of the functional coefficient and the smooth functions are considered, and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions. Some simulation results and a real data example are presented to illustrate the performance of our estimation method.

关 键 词：functional linear model sieve estimator SPLINE knot number convergence rate 

分 类 号：O212[理学—概率论与数理统计]