Table 1.
Empirical Type I errors and powers 
of various tests for normal samples with 
, 
and covariance matrix 
. Zero signal strength 
represents Type I errors, while 
represents powers; the results outside and inside parentheses were calculated from asymptotics- and permutation-based 
-values, respectively. The sparsity parameter was 
, leading to 117 nonzero elements in 
with a constant value of 
| Test |  |
 |
 |
 |
 |
|---|---|---|---|---|---|
| SPU(1) | 5 (5) | 50 (46) | 78 (76) | 92 (91) | 98 (97) |
| SPU(2) | 5 (5) | 22 (20) | 47 (46) | 69 (67) | 87 (85) |
| SPU(3) | 4 (4) | 40 (40) | 71 (70) | 88 (89) | 97 (97) |
| SPU(4) | 5 (5) | 19 (18) | 38 (37) | 61 (60) | 79 (78) |
| SPU(5) | 4 (5) | 24 (25) | 47 (49) | 70 (72) | 84 (86) |
| SPU(6) | 4 (4) | 13 (14) | 26 (29) | 42 (45) | 60 (64) |
SPU( ) |
6 (5) | 12 (9) | 18 (15) | 25 (21) | 35 (28) |
| aSPU | 6 (5) | 33 (34) | 66 (66) | 85 (85) | 94 (94) |
| CLZ | 12 (5) | 33 (15) | 56 (34) | 77 (57) | 91 (76) |
| CLX | 6 (5) | 12 (9) | 18 (15) | 25 (21) | 35 (28) |
| BS | 6 (5) | 23 (20) | 48 (46) | 70 (67) | 88 (85) |
| CQ | 6 (5) | 23 (20) | 48 (46) | 70 (67) | 88 (85) |
| SD | 4 (5) | 19 (19) | 43 (45) | 67 (68) | 85 (86) |
SPU, the proposed sum-of-powers tests with different values of 
; aSPU, the
adaptive sum-of-powers test; CLZ, test of Chen et al. (2014); CLX, test of
Cai et al. (2014); BS, test of Bai & Saranadasa (1996); CQ, test of Chen &
Qin (2010); SD, test of Srivastava & Du (2008).