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Econometrics 2016, 4(4), 48; doi:10.3390/econometrics4040048

Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency

Department of Economics, Michigan State University, 486W Circle Dr, East Lansing, MI 48824, USA
Academic Editor: Marc S. Paolella
Received: 21 September 2016 / Revised: 15 November 2016 / Accepted: 23 November 2016 / Published: 8 December 2016
View Full-Text   |   Download PDF [917 KB, uploaded 8 December 2016]

Abstract

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically-bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies that at least in terms of the third-order stochastic expansion, we cannot improve on the simple one-step bias correction by using the bias correction of moment equations. This finding suggests that the comparison between the one-step bias correction and the method of correcting the moment equations or the fully-iterated bias correction should be based on the stochastic expansions higher than the third order. View Full-Text
Keywords: third-order stochastic expansion; bias correction; M-estimation third-order stochastic expansion; bias correction; M-estimation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Kim, K.I. Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency. Econometrics 2016, 4, 48.

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