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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
Econometrics 2016, 4(4), 48; https://doi.org/10.3390/econometrics4040048
Received: 21 September 2016 / Revised: 15 November 2016 / Accepted: 23 November 2016 / Published: 8 December 2016
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
MDPI and ACS Style

Kim, K.I. Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency. Econometrics 2016, 4, 48. https://doi.org/10.3390/econometrics4040048

AMA Style

Kim KI. Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency. Econometrics. 2016; 4(4):48. https://doi.org/10.3390/econometrics4040048

Chicago/Turabian Style

Kim, Kyoo I. 2016. "Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency" Econometrics 4, no. 4: 48. https://doi.org/10.3390/econometrics4040048

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Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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