(a) \(-1/+1/pen\) systems with various \(pen\) for \(\lambda_0=0.05\)
\(pen\) 0 1 2 3
Level \(\ell\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\)
9 17.096 0.001 12.635 0.002 10.288 0.004 8.801 0.008
8 13.947 0.000 9.626 0.001 7.468 0.002 6.151 0.002
7 11.978 0.000 8.413 0.001 6.597 0.002 5.477 0.002
6 10.384 0.000 7.331 0.001 5.786 0.002 4.832 0.003
5 9.408 0.001 6.282 0.001 4.985 0.003 4.187 0.004
4 7.304 0.001 5.197 0.002 4.159 0.004 3.520 0.006
3 5.552 0.002 4.035 0.005 3.284 0.008 2.815 0.012
2 3.676 0.007 2.816 0.015 2.367 0.023 2.076 0.030
1 2.003 0.044 1.676 0.073 1.483 0.095 1.348 0.111
0 0.887 0.944 0.826 0.898 0.779 0.858 0.740 0.821
HMSE 0.00287 0.00249 0.00227 0.00213

(b) \(-1/+2/pen\) systems with various \(pen\) for \(\lambda_0=0.05\)
\(pen\) 0 1 2 3
Level \(\ell\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\)
9 10.288 0.002 8.105 0.007 6.858 0.013 6.030 0.020
8 8.106 0.002 5.793 0.004 4.567 0.005 3.807 0.007
7 6.755 0.002 5.101 0.004 4.209 0.005 3.633 0.006
6 5.410 0.003 4.006 0.005 3.263 0.008 2.796 0.011
5 4.638 0.003 3.674 0.005 3.135 0.007 2.772 0.008
4 3.349 0.007 2.599 0.014 2.205 0.020 1.950 0.027
3 2.973 0.009 2.497 0.012 2.206 0.013 2.000 0.014
2 1.779 0.041 1.508 0.066 1.351 0.086 1.241 0.101
1 1.677 0.038 1.512 0.034 1.394 0.030 1.303 0.028
0 0.811 0.892 0.762 0.850 0.723 0.812 0.691 0.778
HMSE 0.00260 0.00244 0.00235 0.00229

(c) \(-1/+1/pen\) systems with various \(pen\) for \(\lambda_0=1\)
\(pen\) 0 1 2 3
Level \(\ell\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\) \(\tilde{\zeta}(\ell)\) \(\mathbb{P}(L=\ell)\)
14 2.092 0.311 1.713 0.463 1.528 0.562 1.416 0.634
13 1.147 0.089 0.791 0.060 0.618 0.045 0.512 0.035
12 0.914 0.044 0.677 0.036 0.546 0.030 0.462 0.025
11 0.794 0.027 0.602 0.025 0.494 0.022 0.422 0.020
10 0.718 0.020 0.548 0.019 0.453 0.018 0.390 0.016
9 0.662 0.016 0.505 0.016 0.419 0.015 0.362 0.014
8 0.618 0.014 0.470 0.015 0.390 0.014 0.337 0.013
7 0.579 0.014 0.439 0.014 0.363 0.014 0.314 0.013
6 0.543 0.014 0.410 0.015 0.339 0.014 0.293 0.013
5 0.508 0.016 0.382 0.016 0.315 0.016 0.273 0.014
4 0.470 0.020 0.353 0.020 0.291 0.018 0.252 0.017
3 0.429 0.027 0.322 0.026 0.266 0.024 0.230 0.021
2 0.380 0.042 0.286 0.038 0.238 0.033 0.207 0.029
1 0.321 0.078 0.246 0.065 0.206 0.053 0.180 0.044
0 0.246 0.269 0.197 0.172 0.169 0.122 0.150 0.091
HMSE 1.08320 1.23048 1.32241 1.38605