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Statistical inferences for partially linear single-index models with error-prone linear covariates
Authors:Zhensheng Huang
Affiliation:School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, PR China
Abstract:
We consider statistical inference for partially linear single-index models (PLSIM) when some linear covariates are not observed, but ancillary variables are available. Based on the profile least-squared estimators of the unknowns, we study the testing problems for parametric components in the proposed models. It is to see whether the generalized likelihood ratio (GLR) tests proposed by Fan et al. (2001) are applicable to testing for the parametric components. We show that under the null hypothesis the proposed GLR statistics follow asymptotically the χ2-distributions with the scale constants and the degrees of freedom being independent of the nuisance parameters or functions, which is called the Wilks phenomenon. Simulated experiments are conducted to illustrate our proposed methodology.
Keywords:Ancillary variables   Generalized likelihood ratio test   Local linear method   Partially linear single-index models   Wilks phenomenon
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