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. Author manuscript; available in PMC: 2017 Apr 1.
Published in final edited form as: Ann Stat. 2016 Apr;44(2):629–659. doi: 10.1214/15-AOS1380

Table 4.

Numerical comparison of LLA and the proposed MIPGO on LR-SCAD and LR-MCP problems with different problem scales. “TS” stands for “Typical Sample”.

MIPGO LLAr gap(%) LLA0 gap(%) LLA1 gap(%)
LR-SCAD
TS 3 Min. 89.87 89.87 0.00 104.96 14.37 104.96 14.37
d = 10 Ave. 89.87 109.19 17.69 104.96 14.37 104.96 14.37
n = 10 Max. 89.87 162.93 44.84 104.96 14.37 104.96 14.37
TS 6 Min. 86.04 88.219 2.46 115.17 25.30 108.37 20.60
d = 20 Ave. 86.04 105.13 18.15 115.17 25.30 108.37 20.60
n = 10 Max. 86.04 143.51 40.05 115.17 25.30 108.37 20.60
TS 9 Min. 120.35 120.35 0.00 150.15 19.85 120.35 0.00
d = 40 Ave. 120.35 167.21 28.02 150.15 19.85 120.35 0.00
n = 15 Max. 120.35 203.18 40.76 150.15 19.85 120.35 0.00
TS 12 Min. 519.14 519.14 0.00 560.28 7.34 538.47 3.59
d = 200 Ave. 519.14 733.06 29.18 560.28 7.34 538.47 3.59
n = 60 Max. 519.14 959.00 45.87 560.28 7.34 538.47 3.59
TS 15 Min. 841.72 841.90 0.02 1003.69 16.14 873.44 3.63
d = 500 Ave. 841.72 981.73 14.26 1003.69 16.14 873.44 3.63
n = 80 Max. 841.72 1173.06 28.25 1003.69 16.14 873.44 3.63
TS 18 Min. 1045.22 1105.70 5.47 1119.84 6.66 1119.84 6.66
d = 1000 Ave. 1045.22 1135.84 7.98 1119.84 6.66 1119.84 6.66
n = 100 Max. 1045.22 1309.70 20.19 1119.84 6.66 1119.84 6.66
LR-MCP
TS 3 Min. 13.65 15.77 13.43 21.51 36.54 25.00 45.39
d = 10 Ave. 13.65 20.60 39.59 21.51 36.54 25.00 45.39
n = 10 Max. 13.65 32.83 58.41 21.51 36.54 25.00 45.39
TS 6 Min. 14.71 17.60 16.41 14.71 0.00 20.06 26.67
d = 20 Ave. 14.71 17.60 22.54 14.71 0.00 20.06 26.67
n = 10 Max. 14.71 17.60 65.38 14.71 0.00 20.06 26.67
TS 9 Min. 23.64 27.17 13.02 26.57 11.05 49.08 51.84
d = 40 Ave. 23.64 27.17 35.40 26.57 11.05 49.08 51.84
n = 15 Max. 23.64 27.17 57.98 26.57 11.05 49.08 51.84
TS 12 Min. 93.55 105.62 11.42 112.13 16.57 120.63 22.45
d = 200 Ave. 93.55 165.25 43.39 112.13 16.57 120.63 22.45
n = 60 Max. 93.55 596.52 84.32 112.13 16.57 120.63 22.45
TS 15 Min. 163.98 175.44 6.53 221.84 26.08 179.53 8.66
d = 500 Ave. 163.98 211.62 22.51 221.84 26.08 179.53 8.66
n = 80 Max. 163.98 237.56 30.97 221.84 26.08 179.53 8.66
TS 18 Min. 249.89 267.83 6.70 267.83 6.70 272.39 8.27
d = 1000 Ave. 249.89 322.24 22.25 267.83 6.70 272.39 8.27
n = 100 Max. 249.89 530.60 52.60 267.83 6.70 272.39 8.27