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. Author manuscript; available in PMC: 2011 May 18.
Published in final edited form as: J Am Stat Assoc. 2008 Dec 1;103(484):1693–1704. doi: 10.1198/016214508000001084

Table 1.

Bias, variance, empirical variance and Type I error rate (α) of tests performed at the 5% signi cance level.

(δ, λ) Estimator Bias Variance Empirical Var α
(0,0) ACE 9 10-5 0.0023 0.0023 0.045
CI 6 10-4 0.0025 0.0024 0.037
G 8 10-4 0.00067 0.00072 0.066
OLS 4 10-4 0.00041 0.00042 0.058
NI 6 10-4 - 0.0010 -

(0,-2) ACE 9 10-5 0.0023 0.0023 0.045
CI -0.024 0.14 0.11 0.066
G 1.32 0.0056 0.0058 1.00
OLS 2.40 0.0050 0.019 1.00
NI 0.063 - 0.028 -

(1,0) ACE 3 10-4 0.0013 0.0013 0.050
CI 3 10-3 0.00059 0.00052 0.053
G 1 10-4 0.00028 0.00029 0.054
OLS 5 10-5 0.00023 0.00023 0.050
NI 5 10-4 - 0.0011 -

(1,-2) ACE 0.00029 0.0013 0.0013 0.050
CI 0.12 0.016 0.016 0.24
G 0.57 0.0062 0.0063 1.00
OLS 1.33 0.0056 0.029 1.00
NI -0.30 - 0.035 -