Table 4.
Performance of estimators when p1−q1 ≠ (1−q1)(p2−q2). Coverage is the empirical coverage of the nominal 95% confidence interval and length is the average length of the 95% confidence interval. Allocation a = 0.35.
p1 = .4, q1 = .2, p2 = .4, q2 = .1 | p1 = .4, q1 = .2, p2 = .3, q2 = .1 | ||||||||||
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n | Estimator | Bias | Variance | MSE | Coverage | Length | Bias | Variance | MSE | Coverage | Length |
50 | MLE | -.002 | .022 | .022 | 92 | 0.555 | .008 | .024 | .024 | 93 | 0.554 |
CMLE | .042 | .013 | .014 | 89 | 0.402 | .002 | .011 | .011 | 92 | 0.388 | |
O | .021 | .010 | .011 | 94 | 0.382 | -.023 | .009 | .009 | 95 | 0.366 | |
EST | .019 | .011 | .012 | 90 | 0.366 | -.027 | .010 | .010 | 90 | 0.347 | |
WA | .021 | .010 | .011 | 92 | 0.370 | -.022 | .009 | .009 | 92 | 0.353 | |
Range SE | .003- | .0005- | .0005- | .8- | .0000- | .003- | .0004- | .0004- | .7- | .0000- | |
.005 | .0010 | .0010 | .10 | .0013 | .005 | .0011 | .0011 | 1.0 | .0013 | ||
| |||||||||||
100 | MLE | .001 | .010 | .010 | 93 | 0.391 | .001 | .010 | .010 | 93 | 0.391 |
CMLE | .043 | .006 | .008 | 89 | 0.287 | .000 | .006 | .006 | 94 | 0.279 | |
O | .021 | .005 | .005 | 93 | 0.270 | -.024 | .005 | .005 | 93 | 0.259 | |
EST | .020 | .005 | .006 | 92 | 0.265 | -.025 | .005 | .005 | 91 | 0.253 | |
WA | .021 | .005 | .005 | 93 | 0.266 | -.024 | .005 | .005 | 92 | 0.255 | |
Range SE | .002- | .0002- | .0002- | .8- | .0000- | .002- | .0002- | .0002- | .7- | .0000- | |
.003 | .0005 | .0004 | 1.0 | .0005 | .003 | .0005 | .0005 | .9 | .0005 | ||
| |||||||||||
200 | MLE | -.002 | .005 | .005 | 93 | 0.279 | -.003 | .005 | .005 | 95 | 0.279 |
CMLE | .045 | .003 | .005 | 85 | 0.204 | .001 | .003 | .003 | 94 | 0.199 | |
O | .021 | .002 | .003 | 93 | 0.191 | -.023 | .002 | .003 | 92 | 0.183 | |
EST | .021 | .003 | .003 | 92 | 0.189 | -.023 | .002 | .003 | 91 | 0.182 | |
WA | .022 | .002 | .003 | 93 | 0.189 | -.023 | .002 | .003 | 91 | 0.182 | |
Range SE | .002- | .0001- | .0001- | .8- | .0000 | .002- | .0001- | .0001- | .7- | .0000- | |
.002 | .0002 | .0002 | 1.1 | .0003 | .002 | .0002 | .0002 | .9 | .0003 | ||
| |||||||||||
400 | MLE | -.001 | .003 | .003 | 95 | 0.198 | .000 | .002 | .002 | 94 | 0.198 |
CMLE | .044 | .001 | .003 | 79 | 0.145 | .000 | .001 | .001 | 96 | 0.141 | |
O | .021 | .001 | .002 | 92 | 0.135 | -.024 | .001 | .002 | 89 | 0.130 | |
EST | .021 | .001 | .002 | 92 | 0.135 | -.025 | .001 | .002 | 88 | 0.129 | |
WA | .022 | .001 | .002 | 92 | 0.135 | -.024 | .001 | .002 | 89 | 0.129 | |
Range SE | .001- | <.0001- | <.0001- | .7- | .0000- | .001- | <.0001- | <.0001- | .7- | .0000- | |
.002 | .0001 | .0001 | 1.3 | .0001 | .002 | .0001 | .0001 | 1.0 | .0001 |