Table 6 Estimated MSE for different estimators at p = 6 and \(\phi =4\).

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

5.70916

4.93744

4.28906

4.81213

3.08376

2.50145

1.98185

0.95094

0.63230

2.58249

1.06594

75

1.69674

1.20216

0.85119

1.14056

0.69408

0.56191

0.40785

0.15666

0.13575

0.49567

0.17038

150

0.76054

0.61209

0.51674

0.59309

0.38762

0.32124

0.24519

0.10356

0.08370

0.27317

0.11403

200

0.57336

0.53693

0.50523

0.52987

0.37279

0.31549

0.25467

0.11644

0.08291

0.28135

0.13093

300

0.33520

0.30553

0.28201

0.29455

0.18805

0.15845

0.12323

0.05820

0.05305

0.12744

0.06198

400

0.21962

0.21365

0.20799

0.21025

0.14715

0.12606

0.10289

0.05148

0.04220

0.10634

0.05618

0.85

30

8.46109

7.14163

5.98629

6.66511

3.36577

2.65362

2.05185

0.92821

0.60414

2.81312

1.04919

75

2.25170

1.70572

1.30270

1.65262

1.02561

0.82426

0.60991

0.22394

0.16378

0.76412

0.25451

150

0.76991

0.69548

0.63584

0.68730

0.46873

0.39184

0.30999

0.13259

0.09227

0.35378

0.15029

200

0.65829

0.59368

0.54180

0.58487

0.38573

0.31983

0.24960

0.10185

0.07220

0.27808

0.11582

300

0.45626

0.41454

0.38100

0.40409

0.26327

0.21911

0.17033

0.07256

0.05704

0.18436

0.08067

400

0.31913

0.30758

0.29685

0.30246

0.21126

0.17916

0.14462

0.06504

0.04722

0.15296

0.07319

0.90

30

11.46938

9.41220

7.72538

8.74723

4.68385

3.59193

2.66762

1.03873

0.63890

3.93899

1.20112

75

2.42968

2.07989

1.79738

2.08476

1.39272

1.14437

0.90189

0.39664

0.26433

1.12924

0.44997

150

1.25033

0.99579

0.81721

0.98780

0.63142

0.51123

0.38311

0.13839

0.09637

0.45726

0.15935

200

0.95100

0.85094

0.76887

0.84870

0.56330

0.46049

0.35698

0.13837

0.09038

0.41769

0.16019

300

0.64643

0.58445

0.53368

0.57591

0.37684

0.30876

0.23825

0.09136

0.06143

0.27023

0.10544

400

0.50014

0.47268

0.44763

0.46576

0.31575

0.26067

0.20477

0.08205

0.05476

0.22563

0.09457

0.95

30

38.58210

32.28457

27.12338

29.96805

11.79339

8.76006

6.44526

2.66813

1.61814

10.74345

3.05467

75

4.87018

3.73969

2.86747

3.54226

2.00294

1.54897

1.10800

0.35146

0.22295

1.56029

0.41418

150

2.65203

2.12344

1.71606

2.11806

1.27725

1.00682

0.74042

0.24623

0.15068

0.97164

0.29095

200

1.98940

1.44749

1.06547

1.43288

0.81690

0.63415

0.44520

0.12608

0.08182

0.57153

0.15021

300

1.16438

1.04569

0.94557

1.04668

0.67812

0.54491

0.41578

0.15191

0.09252

0.50337

0.17826

400

0.91651

0.77584

0.67044

0.76989

0.46213

0.36596

0.26767

0.08364

0.05228

0.31288

0.09943

0.99

30

86.84169

74.29102

63.57600

70.46644

33.87303

25.75647

19.69364

9.34368

5.99847

32.73497

10.50118

75

35.09694

28.43725

22.85759

26.33208

11.09987

7.91067

5.44613

1.70266

0.92544

10.06332

2.03519

150

12.67409

10.31242

8.31080

10.09648

4.95917

3.57352

2.44390

0.66887

0.55196

4.07855

0.81918

200

9.01714

7.59321

6.37332

7.53075

4.04242

3.00462

2.14228

0.67853

0.36244

3.34492

0.81598

300

5.98490

4.77790

3.77690

4.71455

2.36668

1.73272

1.18620

0.31455

0.17060

1.81922

0.38567

400

4.12574

3.33075

2.67274

3.33279

1.76216

1.30033

0.90189

0.25244

0.13618

1.31595

0.30738

  1. Bolded values indicate the lowest MSE.
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