湖北民族大学学报（自然科学版）2026，Vol.44Issue(2)：261-271,11.DOI:10.13501/j.cnki.42-1908/n.2026.03.015
部分函数型线性可加模型序列相关检验
Testing for Serial Correlation in Partially Functional Linear Additive Models
摘要
Abstract
This paper addressed the problem of testing the serial correlation of random error terms in partially functional linear additive models.Firstly,the slope function and the additive function were approximated using functional principal component basis functions and B-spline basis functions,respectively,and the quantile regression approach was used for parameter estimation.Secondly,the VT,p test statistic and the data-adaptive empirical likelihood ratio test statistic were constructed.Finally,regularity conditions were established and the asymptotic distributions of the two test statistics were derived.The numerical simulation results showed that under the null hypothesis,both test statistics had test levels that converged well to the significance level;under the alternative hypothesis,as the sample size increased and the strength of serial correlation rose,the power of both test statistics was significantly improved and quickly approached 1.When applied to testing for serial correlation in spectral data,the results indicated that the error sequence exhibited first-order correlation.The two constructed test statistics were demonstrated to have good test levels and power in finite samples and were shown to have practical application value.关键词
部分函数型线性可加模型/序列相关检验/VT,p检验统计量/经验似然比检验统计量/检验水平Key words
partially functional linear additive model/serial correlation test/VT,p test statistic/empirical likelihood ratio test statistic/power of test分类
数理科学引用本文复制引用
李明艳,黄介武,赵庭,雷启贵..部分函数型线性可加模型序列相关检验[J].湖北民族大学学报（自然科学版）,2026,44(2):261-271,11.基金项目
国家自然科学基金项目(62266013) （62266013）
贵州省教育厅自然科学研究项目(黔教技[2022]015号). （黔教技[2022]015号）
