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Enhancements of non-parametric generalized likelihood ratio test: bias correction and dimension reduction. (English) Zbl 1411.62115
In the non-parametric generalized likelihood ratio (NGLR) test, introduced by J. Fan et al. [Ann. Stat. 29, No. 1, 153–193 (2001; Zbl 1029.62042)], a kind of parametric model (null hypothesis) opposes an alternative general non-parametric regression model. In this paper, the authors improve the classical NGLR test by reducing both the bias and dimensionality. The adaptive-to-model enhancement versions of the NGLR tests without bias reduction and with bias reduction are constructed. Note that, the developed method for bias reduction is significantly different from other known techniques. Relevant asymptotic properties under the null hypothesis and under the alternative hypothesis are further highlighted. All proofs are carefully written. The power of the proposed tests is illustrated by an ample simulation study.

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62J12 Generalized linear models (logistic models)
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