Table 8 Estimated MSE values for different estimators at \(p=10\) and \(\varphi =0.5\).

From: A bias-reduced estimator for generalized Poisson regression with application to carbon dioxide emission in Canada

\(\rho\)

n

GPMLE

GPRRE

–

\(\hat{k}^*_{1 }\)

\(\hat{k}^*_{2 }\)

\(\hat{k}^*_{3 }\)

\(\hat{k}^*_{4 }\)

\(\hat{k}^*_{5 }\)

\(\hat{k}^*_{6 }\)

\(\hat{k}^*_{7 }\)

\(\hat{k}^*_{8 }\)

\(\hat{k}^*_{9 }\)

\(\hat{k}^*_{10}\)

\(\hat{k}^*_{11}\)

\(\hat{k}^*_{12}\)

\(\hat{k}^*_{13}\)

\(\hat{k}^*_{14}\)

\(\hat{k}^*_{15}\)

0.80

50

10.0413

6.5984

5.6933

5.6933

3.3771

1.9264

7.5501

6.4572

1.3362

2.5071

3.7315

8.6925

0.6424

0.7781

0.9773

0.8511

 

150

1.7898

1.5391

1.2726

1.2726

1.4750

0.7910

1.3252

1.3288

0.7133

1.4068

1.1779

0.7170

0.3250

0.4996

0.5227

0.4449

 

150

1.0541

0.8711

0.7401

0.7401

0.9291

0.5143

0.7716

0.8520

0.5187

0.9363

0.8098

0.5084

0.2273

0.3764

0.4125

0.3334

 

200

0.6941

0.6362

0.5880

0.5880

0.6478

0.3576

0.5902

0.6117

0.3941

0.6507

0.5853

0.3949

0.1795

0.2471

0.2206

0.1835

 

300

0.4091

0.3878

0.3694

0.3694

0.3944

0.2267

0.3698

0.3782

0.2687

0.3959

0.3691

0.2794

0.1394

0.1691

0.1459

0.1401

 

400

0.3359

0.3194

0.3040

0.3040

0.3250

0.1912

0.3042

0.3134

0.2296

0.3273

0.3096

0.2408

0.1225

0.1448

0.1254

0.1254

0.85

50

11.2624

6.9740

5.9049

5.9049

3.3051

2.0109

7.2177

6.8487

1.3386

2.4649

2.4821

2.2982

0.5955

0.8259

1.0479

0.9365

 

150

3.0234

2.0703

1.5728

1.5728

2.0213

1.2002

1.9317

2.0745

0.9207

1.9218

1.6007

1.0067

0.3553

0.5881

0.7833

0.6891

 

150

1.2829

1.1406

0.9953

0.9953

1.1259

0.6032

1.0124

1.0332

0.5844

1.1077

0.9241

0.5861

0.2482

0.3447

0.3312

0.2698

 

200

1.1445

1.0240

0.8864

0.8864

1.0280

0.5791

0.8971

0.9324

0.5718

1.0175

0.8745

0.5568

0.2259

0.2840

0.2793

0.2294

 

300

0.6448

0.6033

0.5651

0.5651

0.6072

0.3361

0.5656

0.5751

0.3725

0.6087

0.5514

0.3796

0.1492

0.1621

0.1385

0.1317

 

400

0.4413

0.4207

0.4007

0.4007

0.4251

0.2426

0.4008

0.4060

0.2871

0.4263

0.3963

0.2971

0.1249

0.1355

0.1170

0.1248

0.90

50

21.2886

14.8412

13.7362

13.7362

4.8245

3.2693

13.9964

14.1815

1.7533

2.6035

3.1982

4.5273

0.8007

0.8366

1.1202

0.9984

 

150

5.2755

3.7706

2.8606

2.8606

2.8511

1.8235

3.4791

3.4300

1.1671

2.3215

1.9960

1.4843

0.4349

0.6061

0.8008

0.7206

 

150

2.2256

1.8223

1.4441

1.4441

1.7593

0.9923

1.5524

1.6225

0.8258

1.6793

1.3836

0.8397

0.3248

0.3312

0.3886

0.3278

 

200

1.6677

1.4419

1.1726

1.1726

1.4070

0.8078

1.2136

1.2558

0.7098

1.3659

1.1189

0.6885

0.2836

0.2831

0.3001

0.2494

 

300

0.9812

0.8908

0.7858

0.7858

0.8934

0.5094

0.7892

0.8168

0.5111

0.8894

0.7711

0.4933

0.1997

0.1767

0.1638

0.1402

 

400

0.6979

0.6552

0.6080

0.6080

0.6576

0.3736

0.6085

0.6134

0.4056

0.6560

0.5917

0.4035

0.1561

0.1244

0.1083

0.1108

0.95

50

46.2000

29.1804

25.2659

25.2659

5.4837

5.8644

30.2338

28.4016

2.0015

1.9057

3.2731

21.5943

1.0508

0.8383

1.2761

1.1310

 

150

7.7996

5.9213

4.5311

4.5311

3.7790

2.7474

5.2810

5.0166

1.4398

2.5307

2.1785

2.0708

0.7427

0.5808

0.8271

0.7487

 

150

4.9747

3.9420

2.9481

2.9481

3.1353

2.0870

3.3786

3.2766

1.3085

2.4907

2.0358

1.5181

0.6213

0.3795

0.5363

0.4824

 

200

2.7902

2.3894

1.8350

1.8350

2.1707

1.3487

1.9560

1.9215

0.9977

1.9515

1.4803

0.9913

0.4586

0.2909

0.3492

0.3010

 

300

1.9752

1.7565

1.4396

1.4396

1.6631

0.9894

1.4677

1.4550

0.8212

1.5677

1.2487

0.7804

0.3680

0.1622

0.1709

0.1474

 

400

1.3726

1.2224

1.0014

1.0014

1.2074

0.7226

1.0184

1.0661

0.6598

1.1884

1.0039

0.6259

0.2731

0.1312

0.1324

0.1143

0.99

50

224.6266

133.1416

117.7330

117.7330

6.4006

23.3219

145.6016

134.0307

2.7253

0.5511

2.4014

38.1833

1.0479

0.8056

1.5100

1.3295

 

150

45.6679

32.1013

25.0650

25.0650

5.4541

12.3144

30.2648

29.2505

2.0631

0.9091

1.8923

10.6451

1.2642

0.5692

1.1834

1.0402

 

150

26.6899

21.1364

16.5910

16.5910

6.3364

8.4746

18.6381

17.0394

2.0629

1.4275

2.0042

6.5258

1.7247

0.3591

0.7869

0.6792

 

200

16.5518

12.9521

9.6456

9.6456

5.4292

5.9350

11.1317

10.3195

1.9041

1.9134

2.0424

4.1712

1.2661

0.2514

0.5495

0.4835

 

300

8.5828

7.1642

5.3534

5.3534

4.6558

3.6995

5.9379

5.4118

1.7028

2.5801

2.1512

2.4129

1.3575

0.1367

0.2615

0.2337

 

400

6.7322

5.6428

4.1643

4.1643

3.9672

2.9926

4.6288

4.2021

1.5484

2.5519

2.0452

1.9070

1.2166

0.1068

0.1880

0.1731

  1. Bold values indicate the minimum MSE.
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