Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors

作者：Chen Jia; Li Degui^*; Lin Zhengyan

来源：Journal of Statistical Planning and Inference, 2011, 141(9): 3035-3046.

DOI：10.1016/j.jspi.2011.03.025

• Asymptotic expansion
• Long-memory linear processes
• Nonparametric M-estimator

We consider asymptotic expansion of the nonparametric M-estimator in a fixed-design nonlinear regression model when the errors are generated by long-memory linear processes. Under mild conditions, we show that the nonparametric M-estimator is first-order equivalent to the Nadaraya-Watson (NW) estimator, which implies that the nonparametric M-estimator has the same asymptotic distribution as that of the NW estimator. Furthermore, we study the second-order asymptotic expansion of the nonparametric M-estimator and show that the difference between the nonparametric M-estimator and the NW estimator has a limiting distribution after suitable standardization. The nature of the limiting distribution depends on the range of long-memory parameter alpha. We also compare the finite sample behavior of the two estimators through a numerical example when the errors are long-memory.

• 出版日期2011-9
• 单位浙江大学