Wei, Chuanhua; Wu, Xizhi Testing linearity for nonparametric component of partially linear models. (English) Zbl 1125.62044 Math. Appl. 20, No. 1, 183-190 (2007). Summary: In the problem of testing whether the nonparametric component of a partially linear model is a polynomial of a certain degree (denoted \(p\)), we propose a simple test statistic which is based on the sample variance of the estimated \(p\)th derivative of the nonparametric function at each design point. Three-moment \(\chi^2\) approximation is employed to derive the \(p\)-value of the test. Furthermore, some simulations are conducted to examine the performance of our test procedure and the results are satisfactory. Cited in 1 Document MSC: 62G10 Nonparametric hypothesis testing 62G08 Nonparametric regression and quantile regression Keywords:derivative estimation; partially linear models; profile least-squares approach PDFBibTeX XMLCite \textit{C. Wei} and \textit{X. Wu}, Math. Appl. 20, No. 1, 183--190 (2007; Zbl 1125.62044)