Bias-corrected smoothed score function for single-index models |
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Authors: | Qiang Chen Lu Lin Lixing Zhu |
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Institution: | 1. School of Mathematics, Shandong University, Jinan, China 2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
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Abstract: | We in this paper investigate smoothed score function based confidence regions for parameters in single-index models. Because
a plug-in estimator of nonparametric link function causes the bias of smoothed score function to be non-negligible, the limit
of the score function is asymptotically normal with a non-zero mean due to the slow convergence rate of nonparametric estimation.
A bias-corrected smoothed score function is recommended for achieving centered normal limit without under-smoothing or high
order kernel, and then the confidence region can be constructed by chi-square distribution. Simulation studies are carried
out to assess the performance of bias-corrected local likelihood, and to compare with normal approximation approach. |
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Keywords: | |
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