Table 7 Estimated MSE for different estimators at p = 6 and \(\phi =6\).

From: Development of the generalized ridge estimator for the Poisson-Inverse Gaussian regression model with multicollinearity

\(\rho ^2\)

n

PIGMLE

PIGRRE

PIGGRE

MLE

\(\hat{k}_1\)

\(\hat{k}_2\)

\(\hat{k}_3\)

\(\hat{k}_4\)

\(\hat{k}_5\)

\(\hat{K}_1\)

\(\hat{K}_2\)

\(\hat{K}_3\)

\(\hat{K}_4\)

\(\hat{K}_5\)

0.80

30

7.18003

5.96725

4.95220

5.65691

3.43017

2.72024

2.06997

0.84094

0.53800

2.87566

0.96569

75

2.16899

1.49165

0.99617

1.36881

0.84479

0.68046

0.49076

0.18804

0.15851

0.61702

0.20495

150

0.86676

0.65707

0.52660

0.62939

0.39995

0.32912

0.24483

0.09814

0.08226

0.27872

0.10737

200

0.66804

0.61011

0.56204

0.60211

0.41545

0.34953

0.27908

0.12621

0.09206

0.31281

0.14130

300

0.40789

0.36347

0.33030

0.35021

0.22821

0.19257

0.15029

0.07255

0.06477

0.15840

0.07725

400

0.31116

0.29780

0.28569

0.29244

0.20175

0.17121

0.13784

0.06497

0.05267

0.14408

0.07151

0.85

30

10.14016

8.48593

7.04951

7.88894

4.06232

3.18657

2.45156

1.11959

0.77145

3.43226

1.25556

75

2.68506

1.90842

1.35977

1.77110

1.07970

0.86152

0.62508

0.22662

0.17170

0.80587

0.25533

150

0.98303

0.85630

0.75711

0.84855

0.55362

0.45568

0.35068

0.13520

0.09582

0.40985

0.15471

200

0.85518

0.73529

0.64939

0.72495

0.47859

0.39667

0.30818

0.12716

0.08925

0.35018

0.14409

300

0.60915

0.53869

0.48518

0.52807

0.34403

0.28468

0.22019

0.09294

0.07253

0.24267

0.10348

400

0.37681

0.35578

0.33698

0.34848

0.23258

0.19406

0.15270

0.06486

0.04946

0.16341

0.07279

0.90

30

13.14303

10.60679

8.52664

9.67515

5.15026

4.02647

3.06061

1.38919

0.97241

4.38099

1.55263

75

2.97547

2.46797

2.05120

2.50301

1.63325

1.32316

1.02410

0.42405

0.28170

1.31799

0.48440

150

1.64494

1.28766

1.03472

1.26495

0.79908

0.64378

0.47922

0.17359

0.12091

0.58764

0.19932

200

1.10051

0.95294

0.83500

0.95261

0.61667

0.50022

0.38336

0.14826

0.09859

0.45771

0.17084

300

0.82955

0.71539

0.62936

0.70889

0.45245

0.36832

0.28020

0.10575

0.07320

0.32251

0.12143

400

0.55415

0.51468

0.47972

0.50684

0.33374

0.27466

0.21368

0.08508

0.05906

0.23877

0.09744

0.95

30

47.89147

38.17942

30.49429

34.15357

14.82216

11.25518

8.38152

3.73163

2.37455

13.86783

4.20847

75

5.93897

4.43688

3.26921

4.14677

2.38095

1.85000

1.33513

0.45088

0.28393

1.89978

0.52735

150

3.77671

2.94719

2.29815

2.88179

1.62622

1.25264

0.89004

0.26519

0.16417

1.21939

0.31635

200

2.50137

1.79143

1.28696

1.73304

1.00482

0.78128

0.55048

0.16227

0.10631

0.72471

0.19204

300

1.39646

1.20607

1.05069

1.21629

0.77962

0.62152

0.46969

0.16892

0.10304

0.58134

0.19835

400

1.10468

0.91389

0.77171

0.91029

0.54009

0.42692

0.31007

0.09435

0.05997

0.37108

0.11227

0.99

30

104.99316

88.77856

75.12642

82.60415

33.77235

24.75321

18.05264

7.25678

4.23941

33.20595

8.37287

75

41.75106

32.20102

24.40079

28.96857

10.65210

7.39667

4.84938

1.27197

0.70639

9.76427

1.54692

150

15.15633

12.07267

9.49770

11.59891

5.29019

3.80320

2.55909

0.68119

0.37146

4.41116

0.83063

200

12.85437

10.69363

8.83174

10.47499

5.11777

3.71635

2.57294

0.76477

0.41932

4.22717

0.92073

300

8.18779

6.54940

5.18827

6.43319

3.18094

2.31601

1.58019

0.42582

0.22992

2.49836

0.52003

400

5.38889

4.35928

3.50626

4.33666

2.24028

1.63563

1.11685

0.28836

0.15509

1.69409

0.35542

  1. Bolded values indicate the lowest MSE.
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