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Table 5 Simulation study: Illumina's default method versus rmx estimator

From: Preprocessing of gene expression data by optimally robust estimators

  increased variance positive bias least favorable
  N ( 0 , 9 ) t 3 Cauchy N ( 3 , 1 ) N ( 10 , 1 ) D 3 D 1000
s = 0.01
Location.
MLE 1.787 1.022 42.929 1.119 2.297 1.110 > 104
median 1.526 1.499 1.505 1.537 1.537 1.537 1.537
Illumina 1.093 1.080 1.086 1.138 1.083 1.177 1.083
rmx 1.095 1.084 1.088 1.119 1.091 1.124 1.086
Location and scale:
MLE 12.482 1.699 1243.738 1.801 13.366 1.704 > 105
median & MAD 2.869 2.818 2.828 2.882 2.885 2.885 2.885
Illumina 1.806 1.786 1.796 1.901 1.780 1.994 1.780
rmx 1.755 1.689 1.705 1.764 1.779 1.778 1.779
s = 0.02
Location:
MLE 2.563 1.040 756.039 1.282 4.132 1.264 > 104
median 1.553 1.500 1.510 1.583 1.584 1.584 1.584
Illumina 1.110 1.083 1.091 1.214 1.087 1.310 1.087
rmx 1.107 1.085 1.091 1.170 1.099 1.185 1.089
Location and scale:
MLE 23.974 1.880 22605.549 2.190 26.926 1.995 > 105
median & MAD 2.934 2.824 2.842 2.970 2.977 2.977 2.977
Illumina 1.838 1.794 1.810 2.056 1.780 2.276 1.780
rmx 1.862 1.695 1.724 1.886 1.941 1.930 1.941
s = 0.04
Location:
MLE 4.150 1.080 > 104 1.768 9.587 1.732 > 104
median 1.611 1.502 1.524 1.717 1.720 1.720 1.720
Illumina 1.149 1.096 1.111 1.458 1.102 1.716 1.102
rmx 1.139 1.091 1.102 1.343 1.137 1.413 1.099
Location and scale:
MLE 49.559 2.221 > 105 3.285 59.046 2.879 > 106
median & MAD 3.090 2.833 2.876 3.232 3.256 3.256 3.256
Illumina 1.923 1.816 1.848 2.534 1.787 3.091 1.787
rmx 2.236 1.710 1.781 2.311 2.591 2.485 2.598
  1. Empirical MSE (multiplied by n) for normal location and scale estimators at sample size n = 11 (105 Monte-Carlo replications) and contamination s {0.01, 0.02, 0.04}.