The Local Linear M-Estimator with a Robust Initial Estimate

10.29973/JCSA.200612.0003

Ruey-Ching Hwang；Wen-Shuenn Deng；Chih-Kang Chu

local linear estimator ； local linear M-estimator ； Newton method ； nonparametric regression ； robust initial estimate ； robustness

中國統計學報

44卷4期（2006 / 12 / 01）

382 - 401

英文

In the field of nonparametric regression, the local linear M-estimator (LLM; Fan and Jiang 1999) is proposed to adjust for the unrobustness of the local linear estimator (LLE; Fan 1992, 1993). In practice, the LLM is often computed using Newton method together with an initial estimate produced by the LLE. However, by the unrobustness of the LLE, such initial estimate might be far from the global minimizer of M function. In this case, the Newton method might provide an incorrect solution for the LLM. To improve the drawback, a robust initial estimate for Newton method is proposed. Simulation results show that our robust initial estimate is useful when using Newton method to find a solution for the LLM.

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