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Tests for nonparametric parts on partially linear single index models

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Abstract

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ 2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

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Authors and Affiliations

  1. Department of Statistics, East China Normal University, Shanghai, 200062, China

    Ri-quan Zhang

  2. Department of Mathematics, Shanxi Datong University, Datong, 037009, China

    Ri-quan Zhang

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  1. Ri-quan Zhang
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Zhang, Rq. Tests for nonparametric parts on partially linear single index models. SCI CHINA SER A 50, 439–449 (2007). https://doi.org/10.1007/s11425-007-2059-z

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  • DOI: https://doi.org/10.1007/s11425-007-2059-z

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