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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}.