Table 9 Estimated MSE for robust and non-robust estimators at 10% outliers, \(p=8\), and \(\beta _0=-1\).

From: New robust two-parameter estimator for overcoming outliers and multicollinearity in Poisson regression model

\(\theta\)

n

Non-robust estimator

Robust estimator

PMLE

PRRE

PMRTE

PTPE

PMT

PMT-RRE

PMT-MRTE

PMT-TPE

-

\({\hat{k}}_1\)

\({\hat{k}}_2\)

\({\hat{k}}_1\)

\({\hat{k}}_2\)

\({\hat{k}}_1\)

\({\hat{k}}_2\)

-

\({\hat{k}}_1\)

\({\hat{k}}_2\)

\({\hat{k}}_1\)

\({\hat{k}}_2\)

\({\hat{k}}_1\)

\({\hat{k}}_2\)

0.85

30

9.24468

8.80887

8.53504

8.53504

7.69007

5.72599

5.37831

5.62264

5.25393

4.95916

4.95916

4.38809

3.01407

2.78367

75

3.79193

3.70595

3.60021

3.60021

3.57212

3.35871

3.33915

0.96671

0.91865

0.85969

0.85969

0.85459

0.75283

0.75052

100

2.98261

2.951

2.90773

2.90773

2.91629

2.85179

2.86062

0.43249

0.41794

0.40097

0.40097

0.4051

0.3799

0.38384

200

2.57561

2.56293

2.54578

2.54578

2.55032

2.52505

2.5298

0.17105

0.16979

0.16828

0.16828

0.16876

0.1666

0.16706

300

1.89361

1.89073

1.8889

1.8889

1.8898

1.88583

1.88674

0.07651

0.07651

0.07648

0.07648

0.07649

0.07649

0.07649

400

1.57277

1.57099

1.56986

1.56986

1.57043

1.56798

1.56855

0.05359

0.05385

0.05396

0.05396

0.05389

0.05422

0.05414

0.90

30

16.14988

14.40514

13.68641

13.68641

9.58246

8.33414

7.77839

7.19879

6.62428

6.07832

6.07832

5.39818

4.91964

4.89019

75

5.21724

5.16923

5.09612

5.09612

5.08481

4.9491

4.93976

0.58517

0.57041

0.54957

0.54957

0.55026

0.51698

0.51778

100

3.97745

3.9498

3.90578

3.90578

3.91291

3.84896

3.85638

0.37115

0.36312

0.3519

0.3519

0.35442

0.33852

0.34095

200

2.06394

2.05972

2.05311

2.05311

2.05184

2.0383

2.03714

0.32991

0.32919

0.32806

0.32806

0.32743

0.32441

0.32381

300

1.93475

1.92997

1.92624

1.92624

1.92794

1.92089

1.92266

0.13758

0.13717

0.13666

0.13666

0.13668

0.13582

0.13585

400

1.5233

1.51917

1.51421

1.51421

1.51498

1.5067

1.50753

0.0839

0.08391

0.0839

0.0839

0.0839

0.08392

0.08392

0.95

30

33.13313

30.99214

29.94129

29.94129

21.92505

8.68921

7.45066

12.37094

9.12975

7.96497

7.96497

7.28029

6.33418

5.28013

75

6.01856

5.7262

5.42791

5.42791

5.1605

4.33829

4.17713

2.38252

2.1669

1.93363

1.93363

1.83247

1.38434

1.32659

100

4.98359

4.95238

4.90507

4.90507

4.90113

4.81609

4.81295

0.42532

0.41746

0.40581

0.40581

0.40621

0.38748

0.38792

200

3.36248

3.33756

3.30207

3.30207

3.30646

3.2507

3.25527

0.24176

0.23755

0.23207

0.23207

0.23321

0.22489

0.22601

300

2.65728

2.64288

2.62076

2.62076

2.62584

2.59444

2.59972

0.16494

0.16339

0.1612

0.1612

0.16174

0.15863

0.15917

400

1.86311

1.85555

1.84688

1.84688

1.84935

1.83547

1.83795

0.13784

0.13605

0.13444

0.13444

0.13499

0.13216

0.1327

0.99

30

191.1005

178.74857

172.26102

172.26102

83.71255

11.89341

9.60422

95.48614

81.39036

73.9763

73.9763

68.24092

29.06921

27.2848

75

28.48794

27.02167

25.54074

25.54074

20.18399

18.9101

16.40827

11.85093

10.9902

10.08966

10.08966

7.77096

3.47256

2.79366

100

18.29479

18.03062

17.71758

17.71758

16.83566

13.92143

13.29848

2.99294

2.93642

2.86098

2.86098

2.70598

2.17912

2.07122

200

8.73154

8.62073

8.45171

8.45171

8.24594

7.49625

7.32191

1.46135

1.4414

1.41012

1.41012

1.37734

1.24205

1.21431

300

7.30767

7.24179

7.12629

7.12629

7.04069

6.72642

6.64939

0.59742

0.58942

0.57559

0.57559

0.56628

0.53014

0.52189

400

5.88016

5.82719

5.73104

5.73104

5.68413

5.47101

5.42896

0.40884

0.40333

0.39332

0.39332

0.38937

0.36882

0.36534

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