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Table 3 Simulation study: Tukey's biweight 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 1.51 D 1000
s = 0.01
Location.
MLE 1.802 1.022 300.548 1.100 2.103 1.017 > 104
median 1.554 1.516 1.522 1.551 1.551 1.551 1.551
biweight 1.325 1.316 1.317 1.343 1.319 1.346 1.318
rmx 1.109 1.096 1.098 1.131 1.105 1.117 1.097
Location and scale:
MLE 6.987 1.638 3293.342 1.745 7.616 1.541 > 105
median & MAD 2.919 2.864 2.876 2.930 2.936 2.908 2.936
TuMAD 2.700 2.663 2.671 2.723 2.704 2.703 2.704
rmx 1.811 1.736 1.752 1.804 1.853 1.742 1.855
s = 0.02
Location:
MLE 2.575 1.045 405.083 1.216 3.387 1.037 > 104
median 1.575 1.519 1.528 1.593 1.595 1.595 1.595
biweight 1.339 1.318 1.322 1.380 1.327 1.386 1.326
rmx 1.131 1.100 1.106 1.184 1.135 1.149 1.105
Location and scale:
MLE 12.311 1.756 4439.072 1.975 13.890 1.548 > 105
median & MAD 2.986 2.870 2.892 3.014 3.032 2.963 3.032
TuMAD 2.749 2.669 2.685 2.802 2.764 2.755 2.764
rmx 1.931 1.744 1.777 1.907 2.071 1.761 2.093
s = 0.04
Location:
MLE 4.192 1.096 > 104 1.497 6.557 1.125 > 104
median 1.643 1.526 1.546 1.696 1.701 1.627 1.701
biweight 1.368 1.322 1.331 1.476 1.344 1.415 1.338
rmx 1.182 1.106 1.119 1.326 1.285 1.197 1.116
Location and scale:
MLE 23.633 2.063 > 105 2.513 27.267 1.690 > 105
median & MAD 3.151 2.883 2.930 3.232 3.301 3.030 3.301
TuMAD 2.875 2.680 2.716 3.012 2.944 2.818 2.938
rmx 2.305 1.759 1.828 2.192 2.984 1.858 3.289
  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}.