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. Author manuscript; available in PMC: 2013 Jun 1.
Published in final edited form as: J Am Stat Assoc. 2012 Dec 1;107(500):1310–1323. doi: 10.1080/01621459.2012.695648

Table 2.

(A)Absolute bias for the proposed method and the ratio bias (naive/proposed) and (B) mean square error (MSE) of the naive and the proposed bias-corrected estimates corresponding to Table 1. See Table 1 caption for details.

(A) Bias β 1 β 2 β 3

Pattern Proposed Ratio Proposed Ratio Proposed Ratio
(a) 0.008 8.125 0.006 11.167 0.019 4.105
(b) 0.003 12.333 0.016 3.562 0.020 4.300
(c) 0.008 5.000 0.004 15.500 0.008 12.000
(d) 0.019 4.526 0.031 0.581 0.005 24.200
(e) 0.008 2.125 0.010 1.700 0.010 7.700
(f) 0.003 29.667 0.007 1.143 0.004 21.000
(B) MSE
Pattern Naive Proposed Naive Proposed Naive Proposed
(a) 0.012 0.017 0.017 0.023 0.021 0.030
(b) 0.015 0.032 0.014 0.024 0.018 0.019
(c) 0.013 0.025 0.010 0.014 0.022 0.027
(d) 0.016 0.017 0.012 0.028 0.026 0.017
(e) 0.011 0.026 0.012 0.026 0.021 0.028
(f) 0.017 0.018 0.013 0.031 0.020 0.028