Table 5 Estimated MSE values for different estimators at \(p=7\) 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

3.2325

2.1434

1.8052

1.8052

1.6820

0.9828

2.1016

2.0620

0.7769

1.3945

1.2490

0.9881

0.4157

0.5200

0.6765

0.6007

 

100

0.9011

0.7451

0.6440

0.6440

0.7907

0.4867

0.6595

0.7081

0.4550

0.7571

0.6465

0.4606

0.2551

0.3169

0.3945

0.3410

 

150

0.5856

0.4978

0.4583

0.4583

0.5396

0.3332

0.4570

0.5061

0.3416

0.5332

0.4781

0.3537

0.1767

0.1896

0.2426

0.2058

 

200

0.3863

0.3329

0.3127

0.3127

0.3664

0.2349

0.3125

0.3519

0.2555

0.3661

0.3394

0.2672

0.1393

0.1488

0.1836

0.1585

 

300

0.2693

0.2401

0.2253

0.2253

0.2592

0.1693

0.2258

0.2511

0.1905

0.2597

0.2449

0.2027

0.1075

0.1111

0.1232

0.1136

 

400

0.1980

0.1895

0.1827

0.1827

0.1938

0.1277

0.1828

0.1873

0.1479

0.1932

0.1849

0.1595

0.0948

0.0959

0.0898

0.1024

0.85

50

7.8202

5.3076

4.7770

4.7770

2.4711

1.6676

4.7630

5.1508

1.0122

1.6948

1.6988

1.7863

0.5035

0.5652

0.8339

0.7490

 

100

1.1477

0.9346

0.7998

0.7998

0.9725

0.5824

0.8213

0.8691

0.5162

0.9124

0.7630

0.5363

0.2580

0.2931

0.3774

0.3305

 

150

0.8676

0.6950

0.5965

0.5965

0.7608

0.4585

0.6205

0.6954

0.4312

0.7366

0.6335

0.4446

0.1868

0.1879

0.2488

0.2139

 

200

0.5302

0.4221

0.3749

0.3749

0.4855

0.3101

0.3790

0.4563

0.3177

0.4872

0.4375

0.3270

0.1554

0.1703

0.2464

0.1960

 

300

0.3154

0.2963

0.2826

0.2826

0.3043

0.1914

0.2828

0.2906

0.2137

0.3020

0.2823

0.2279

0.1094

0.1104

0.1030

0.1137

 

400

0.2779

0.2654

0.2563

0.2563

0.2702

0.1700

0.2564

0.2595

0.1945

0.2682

0.2525

0.2090

0.0925

0.0970

0.0869

0.1085

0.90

50

5.9029

3.7296

2.9772

2.9772

2.4956

1.7694

3.6752

3.5626

1.0339

1.6834

1.5897

1.5697

0.5516

0.5983

0.8830

0.8126

 

100

2.2916

1.6298

1.2516

1.2516

1.6366

1.0745

1.4578

1.5253

0.7825

1.3880

1.1410

0.8446

0.3784

0.3644

0.5540

0.5051

 

150

1.3322

1.0759

0.8690

0.8690

1.1143

0.6926

0.9237

0.9682

0.5796

1.0251

0.8445

0.5832

0.2622

0.1983

0.2576

0.2309

 

200

1.0541

0.8927

0.7354

0.7354

0.9238

0.5883

0.7592

0.8054

0.5188

0.8695

0.7508

0.5136

0.2350

0.1540

0.1785

0.1607

 

300

0.6192

0.5526

0.4958

0.4958

0.5725

0.3532

0.4983

0.5264

0.3511

0.5590

0.4978

0.3606

0.1481

0.1062

0.0994

0.1001

 

400

0.4097

0.3451

0.3045

0.3045

0.3844

0.2443

0.3086

0.3667

0.2628

0.3862

0.3557

0.2770

0.1083

0.0917

0.0990

0.0972

0.95

50

10.5843

7.0806

5.9125

5.9125

3.8011

2.8498

6.9864

6.4531

1.3367

1.7615

1.8616

2.6896

0.8338

0.5889

0.9031

0.8234

 

100

3.9217

2.7952

2.1136

2.1136

2.4471

1.7547

2.5055

2.4785

1.0480

1.7062

1.3859

1.2694

0.6122

0.3425

0.5792

0.5387

 

150

2.6906

2.1520

1.6390

1.6390

1.9883

1.3176

1.8054

1.7437

0.8875

1.5214

1.2302

0.9509

0.4792

0.1986

0.2902

0.2718

 

200

1.7517

1.4372

1.1145

1.1145

1.4214

0.9307

1.1920

1.2053

0.7097

1.2315

0.9964

0.7079

0.3597

0.1378

0.1806

0.1665

 

300

1.0475

0.8044

0.6329

0.6329

0.8934

0.5876

0.6839

0.8076

0.5138

0.8666

0.7370

0.5092

0.2225

0.0966

0.1284

0.1143

 

400

0.8092

0.6313

0.5098

0.5098

0.7156

0.4700

0.5394

0.6577

0.4393

0.7082

0.6198

0.4408

0.1808

0.0805

0.0957

0.0885

0.99

50

63.1640

39.9406

33.0709

33.0709

4.2545

12.5910

40.6951

37.4582

1.5280

0.4250

1.1941

13.5719

0.7797

0.5791

1.2742

1.1157

 

100

19.6837

13.3269

10.4364

10.4364

4.9210

6.0585

12.7453

11.8404

1.5031

0.9308

1.4385

5.0314

0.9795

0.2323

0.6602

0.5736

 

150

12.7634

8.3207

6.2424

6.2424

3.9310

4.4185

7.9100

7.6234

1.3548

1.1547

1.4043

3.2993

0.8687

0.1587

0.4670

0.4159

 

200

8.7063

5.0538

3.5677

3.5677

3.1355

3.3136

4.9629

5.1701

1.2420

1.4011

1.3747

2.3261

0.7758

0.1285

0.4192

0.3815

 

300

5.3728

3.3092

2.2601

2.2601

2.7869

2.4599

3.0419

3.2663

1.2150

1.7226

1.4843

1.6332

0.7372

0.0702

0.2124

0.2002

 

400

4.0594

2.8981

1.9895

1.9895

2.5001

1.9594

2.4366

2.4998

1.1080

1.6942

1.3881

1.3062

0.7798

0.0526

0.1050

0.1003

  1. Bold values indicate the minimum MSE.
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