部分函数型线性可加模型序列相关检验OA

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.