Testing for Error Correlation in Semi-Functional Linear Models  

作　　者：YANG Bin CHEN Min ZHOU Jianjun 

机构地区：[1]Yunnan Key Laboratory of Statistical Modeling and Data Analysis,Yunnan University,Kunming 650091,China [2]City College,Kunming University of Science and Technology,Kunming 650051,China [3]School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China [4]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Journal of Systems Science & Complexity》2023年第4期1697-1716,共20页系统科学与复杂性学报（英文版）

基　　金：This research was supported by the National Natural Science Foundation of China under Grant Nos.11861074,11731011,11731015 and 12261051;Applied Basic Research Project of Yunnan Province under Grant No.2019FB138.

摘　　要：Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order.However,in some applications,these assumptions on random errors may be unreasonable or questionable.To this end,this paper aims at testing error correlation in a semi-functional linear model(SFLM).Based on the empirical likelihood approach,the authors construct an empirical likelihood ratio statistic to test the serial correlation of random errors and identify the order of autocorrelation if the serial correlation holds.The proposed test statistic does not need to estimate the variance as it is data adaptive and possesses the nonparametric version of Wilks'theorem.Simulation studies are conducted to investigate the performance of the proposed test procedure.Two real examples are illustrated by the proposed test method.

关 键 词：Empirical likelihood error correlation functional principal component analysis semifunctional linear model spline estimation Wilks'theorem 

分 类 号：O212.1[理学—概率论与数理统计]