Table 4 Estimated MAE for different estimators at \(p=4\).

From: New two parameter hybrid estimator for zero inflated negative binomial regression models

\(\rho ^2\)

n

\(\hat{\beta }_{\text {MLE}}\)

\(\hat{\beta }_{{k}}\)

\(\hat{\beta }_{{d}}\)

\(\hat{\beta }_{{K}}\)

\(\hat{\beta }_{k_m,d_m}\)

\(\hat{\beta }_{k_*,d_*}\)

-

\(\hat{k}_1\)

\(\hat{k}_2\)

\(\hat{k}_3\)

\(\hat{d}\)

\(\hat{K}_1\)

\(\hat{K}_2\)

\(\hat{k_m}_1\)

\(\hat{k_m}_2\)

\(\hat{k_*}_1\)

\(\hat{k_*}_2\)

\(\hat{k_*}_3\)

\(\hat{k_*}_4\)

0.75

30

1.14350

1.07123

1.07985

1.08502

1.08207

1.03766

1.04551

1.03851

1.05357

1.03097

1.02822

1.02786

1.02855

75

0.60681

0.59608

0.59809

0.59894

0.59826

0.58183

0.58815

0.58268

0.59086

0.57714

0.57904

0.57840

0.57697

150

0.38590

0.38211

0.38285

0.38415

0.38324

0.37947

0.38143

0.37956

0.38226

0.37775

0.37923

0.37873

0.37843

200

0.35359

0.35091

0.35145

0.35222

0.35167

0.34838

0.35002

0.34842

0.35052

0.34681

0.34778

0.34737

0.34700

300

0.32022

0.31856

0.31889

0.31932

0.31898

0.31670

0.31784

0.31673

0.31814

0.31568

0.31635

0.31605

0.31583

400

0.29271

0.29154

0.29177

0.29210

0.29185

0.29036

0.29112

0.29037

0.29138

0.28969

0.29027

0.29008

0.28998

0.80

500

0.26774

0.26695

0.26711

0.26726

0.26718

0.26590

0.26649

0.26591

0.26670

0.26547

0.26586

0.26575

0.26569

30

1.15401

1.06780

1.07839

1.08488

1.06124

1.07858

1.06664

1.05270

1.05607

1.06254

1.05686

1.05474

1.06464

75

0.70003

0.68127

0.68446

0.68441

0.68425

0.67227

0.67268

0.67089

0.67427

0.66946

0.66861

0.66901

0.66912

150

0.49651

0.49249

0.49325

0.49354

0.49307

0.48821

0.48992

0.48819

0.49083

0.48672

0.48662

0.48663

0.48616

200

0.43849

0.43653

0.43685

0.43688

0.43673

0.43537

0.43549

0.43526

0.43569

0.43515

0.43447

0.43481

0.43471

300

0.37938

0.37906

0.37905

0.37894

0.37891

0.38044

0.37926

0.38029

0.37902

0.38124

0.38029

0.38072

0.38096

400

0.32906

0.32898

0.32896

0.32896

0.32890

0.32959

0.32916

0.32954

0.32906

0.32980

0.32945

0.32955

0.32956

500

0.33368

0.33433

0.33417

0.33403

0.33407

0.33570

0.33487

0.33567

0.33456

0.33637

0.33584

0.33608

0.33624

0.85

30

1.87032

1.58698

1.63000

1.64360

1.53252

1.37718

1.45194

1.38887

1.50934

1.24819

1.26816

1.25935

1.24436

75

0.96236

0.90267

0.91233

0.90829

0.91621

0.85379

0.86364

0.85556

0.87491

0.84531

0.84603

0.84508

0.84421

150

0.61115

0.60190

0.60343

0.60257

0.60304

0.59642

0.59601

0.59514

0.59680

0.59563

0.59245

0.59395

0.59405

200

0.59770

0.59337

0.59376

0.59230

0.59232

0.60340

0.59479

0.59951

0.59156

0.60499

0.60364

0.60376

0.60648

300

0.51394

0.51568

0.51513

0.51413

0.51433

0.52179

0.51708

0.52093

0.51582

0.52529

0.52245

0.52401

0.52521

400

0.43442

0.43458

0.43449

0.43419

0.43408

0.43688

0.43501

0.43664

0.43441

0.43816

0.43702

0.43756

0.43795

500

0.40936

0.41091

0.41054

0.41023

0.41017

0.41471

0.41237

0.41453

0.41157

0.41642

0.41527

0.41585

0.41636

0.90

30

1.90964

1.64874

1.68713

1.70296

1.58471

1.46897

1.53831

1.46797

1.58121

1.32380

1.33045

1.33298

1.31858

75

1.04018

0.97709

0.98770

0.98415

0.98215

0.93244

0.94103

0.92410

0.94887

0.91180

0.90834

0.91157

0.91071

150

0.80124

0.78177

0.78492

0.78149

0.78067

0.77268

0.76925

0.76689

0.76866

0.77078

0.76670

0.76902

0.77072

200

0.67637

0.66641

0.66778

0.66566

0.66462

0.67234

0.66410

0.66724

0.66140

0.67215

0.66981

0.67116

0.67349

300

0.52875

0.52778

0.52771

0.52651

0.52646

0.53402

0.52839

0.53252

0.52674

0.53723

0.53446

0.53591

0.53741

400

0.48562

0.48444

0.48452

0.48366

0.48384

0.48552

0.48333

0.48497

0.48273

0.48707

0.48492

0.48601

0.48660

500

0.43444

0.43539

0.43510

0.43453

0.43449

0.43906

0.43618

0.43863

0.43537

0.44116

0.43944

0.44026

0.44106

0.95

30

2.43308

1.93700

2.00305

2.05050

1.81445

1.75666

1.83355

1.71602

1.86844

1.57125

1.58684

1.56046

1.58189

75

1.43481

1.25153

1.27856

1.27067

1.25208

1.16813

1.18333

1.15054

1.19382

1.12636

1.12934

1.12544

1.13006

150

1.01359

0.97329

0.97941

0.97492

0.96646

0.97474

0.96162

0.95602

0.95584

0.96629

0.96363

0.96541

0.97155

200

0.90836

0.86918

0.87561

0.87023

0.86356

0.85213

0.84767

0.84013

0.84780

0.84089

0.83651

0.83969

0.84279

300

0.71106

0.69773

0.69970

0.69605

0.69727

0.69873

0.69014

0.69282

0.68780

0.69987

0.69709

0.69827

0.70146

400

0.66806

0.66294

0.66365

0.66117

0.66036

0.66490

0.65914

0.66151

0.65724

0.66718

0.66365

0.66577

0.66782

500

0.59767

0.59281

0.59350

0.59177

0.59213

0.59299

0.58932

0.59176

0.58851

0.59542

0.59416

0.59494

0.59659

0.99

30

5.38293

3.45256

3.67361

3.97252

3.14886

2.88726

3.20253

2.76359

3.34575

2.15895

2.27499

2.04807

2.21088

75

3.08504

2.31319

2.41611

2.48285

1.95392

1.96624

2.11362

1.92947

2.19075

1.63205

1.66343

1.60051

1.65634

150

2.17900

1.76248

1.82215

1.81914

1.66217

1.54194

1.60999

1.52486

1.65125

1.41068

1.42321

1.40924

1.42311

200

1.83579

1.55255

1.59400

1.59664

1.47965

1.42928

1.46549

1.39189

1.47780

1.36580

1.36931

1.36247

1.38372

300

1.50089

1.29098

1.32385

1.31080

1.25555

1.19288

1.20505

1.16024

1.21504

1.14561

1.14448

1.14257

1.15727

400

1.32339

1.20971

1.22866

1.21520

1.19413

1.14683

1.14594

1.12120

1.15349

1.11457

1.11042

1.11349

1.11931

500

1.16682

1.07618

1.09136

1.07833

1.06619

1.02886

1.02287

1.00623

1.02702

1.00487

1.00027

1.00350

1.00923

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