Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-12-01
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| Series: | Econometrics |
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| Online Access: | http://www.mdpi.com/2225-1146/4/4/48 |
| Summary: | 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. |
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| ISSN: | 2225-1146 |