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Inferences on single index models. (English) Zbl 1125.62042

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
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