Bahadur-Kiefer representations for GM-estimators in autoregression models

Hira L. Koul and Zhiwei Zhu

Stochastic Processes and their Applications, 1995, vol. 57, issue 1, 167-189

Abstract: This paper proves strong consistency, along with a rate, of a class of generalized M-estimators for the autoregression parameter vector in pth order autoregression (AR(p)) models. If the score function [psi] has bounded second derivative then the rate of convergence is n-1/2(lnlnn)1/2 while for a general [psi] it is n-1/2(lnn)1/2. The paper also obtains the Bahadur-Kiefer type representations for these estimators. The class of estimators covered includes the least square, the least absolute deviation, and the Huber(k) estimators.

Keywords: Huber(k); and; LAD; estimators; Freedman; inequality (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (4)

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