Table 1 Power for testing \(H_0:\beta ^{(1)}_{j}=\cdots =\beta ^{(G)}_{j}\) vs \(H_1:\) not \(H_0\) at \(\alpha =0.05\), where \(n_1,\ldots ,n_G\) are set as \(n_1=\cdots =n_G=m\).
From: Debiased inference for heterogeneous subpopulations in a high-dimensional logistic regression model
(m, p) | j | \(\min _{g}\beta ^{(g)}_j\) | \(\max _{g}\beta ^{(g)}_j\) | Methods | |||||
|---|---|---|---|---|---|---|---|---|---|
DFGL | DL | DL-E | DR-B | DL-B | DL-E-B | ||||
AR(1) | |||||||||
 (200, 80) | 1 | \(-0.6\) | 0.6 | 0.93 | 0.84 | 0.54 | 0.00 | 0.00 | 0.00 |
2 | \(-\,0.6\) | 0.6 | 0.87 | 0.76 | 0.33 | 0.00 | 0.00 | 0.00 | |
3 | \(-\,0.4\) | 0.6 | 0.62 | 0.44 | 0.21 | 0.00 | 0.00 | 0.00 | |
4 | \(-\,0.4\) | 0.6 | 0.76 | 0.54 | 0.22 | 0.00 | 0.00 | 0.00 | |
 (300, 120) | 1 | \(-\,0.6\) | 0.6 | 1.00 | 0.97 | 0.78 | 0.00 | 0.00 | 0.00 |
2 | \(-\,0.6\) | 0.6 | 0.97 | 0.93 | 0.61 | 0.00 | 0.00 | 0.00 | |
3 | \(-\,0.4\) | 0.6 | 0.90 | 0.75 | 0.44 | 0.00 | 0.00 | 0.00 | |
4 | \(-\,0.4\) | 0.6 | 0.88 | 0.87 | 0.48 | 0.00 | 0.00 | 0.00 | |
Block | |||||||||
 (200, 80) | 1 | \(-\,0.6\) | 0.6 | 0.95 | 0.84 | 0.57 | 0.00 | 0.02 | 0.01 |
2 | \(-\,0.6\) | 0.6 | 0.82 | 0.60 | 0.38 | 0.00 | 0.00 | 0.00 | |
3 | \(-\,0.4\) | 0.6 | 0.66 | 0.44 | 0.20 | 0.00 | 0.00 | 0.00 | |
4 | \(-\,0.4\) | 0.6 | 0.79 | 0.63 | 0.31 | 0.00 | 0.00 | 0.00 | |
 (300, 120) | 1 | \(-\,0.6\) | 0.6 | 1.00 | 0.97 | 0.76 | 0.00 | 0.00 | 0.00 |
2 | \(-\,0.6\) | 0.6 | 0.99 | 0.91 | 0.61 | 0.00 | 0.00 | 0.00 | |
3 | \(-\,0.4\) | 0.6 | 0.88 | 0.78 | 0.40 | 0.00 | 0.00 | 0.00 | |
4 | \(-\,0.4\) | 0.6 | 0.97 | 0.91 | 0.57 | 0.00 | 0.01 | 0.00 | |
