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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}.
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