Han, Fulong; Lu, Yiqiung; Zhang, Riquan Inferences on single index models. (English) Zbl 1125.62042 Adv. Appl. Stat. 6, No. 2, 249-259 (2006). Summary: Estimation of single index models has been discussed. Inferences for link functions of the models are studied. Based on the estimates obtained by local linear methods, generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically a \(\chi^2\)-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters. This is called the Wilks phenomenon. MSC: 62G10 Nonparametric hypothesis testing 62H12 Estimation in multivariate analysis 62G20 Asymptotic properties of nonparametric inference Keywords:local linear method; generalized likelihood ratio test; single index models; Wilks phenomenon PDFBibTeX XMLCite \textit{F. Han} et al., Adv. Appl. Stat. 6, No. 2, 249--259 (2006; Zbl 1125.62042)