Coverage

Lower

Upper

Method

proportion

error

error

1

2

10

Central Limit Theorem

0.5389

0.0003

0.4608

Bootstrap (B = 5000)

0.5582

0.0007

0.4411

Back-transformation

0.1965

0.0000

0.8035

Wald

0.8549

0.0005

0.1446

Third order

0.9460

0.0262

0.0278

50

Central Limit Theorem

0.6907

0.0001

0.3092

Bootstrap (B = 5000)

0.7149

0.0013

0.2838

Back-transformation

0.0000

0.0000

1.0000

Wald

0.9303

0.0034

0.0063

Third order

0.9501

0.0238

0.0261

200

Central Limit Theorem

0.7757

0.0007

0.2236

Bootstrap (B = 5000)

0.7968

0.0021

0.2011

Back-transformation

0.0000

0.0000

1.0000

Wald

0.9446

0.0134

0.0420

Third order

0.9500

0.0261

0.0239

2

0.5

10

Central Limit Theorem

0.8902

0.0129

0.0969

Bootstrap (B = 5000)

0.8793

0.0239

0.078

Back-transformation

0.8884

0.0047

0.1069

Wald

0.8997

0.0246

0.0757

Third order

0.9492

0.0252

0.0256

50

Central Limit Theorem

0.9340

0.0106

0.0554

Bootstrap (B = 5000)

0.9345

0.0197

0.0458

Back-transformation

0.5905

0.0003

0.4092

Wald

0.9415

0.0167

0.0418

Third order

0.9505

0.0231

0.0264

200

Central Limit Theorem

0.9430

0.0172

0.0398

Bootstrap (B = 5000)

0.9466

0.0197

0.0337

Back-transformation

0.0591

0.0000

0.9409

Wald

0.9452

0.0220

0.0328

Third order

0.9481

0.0262

0.0257

3

3

10

Central Limit Theorem

0.2739

0.0000

0.7261

Bootstrap (B = 5000)

0.2842

0.0000

0.7158

Back-transformation

0.0132

0.0000

0.9868

Wald

0.8335

0.0000

0.1665

Third order

0.9465

0.0265

0.0270

50

Central Limit Theorem

0.3983

0.0000

0.6017

Bootstrap (B = 5000)

0.4166

0.0000

0.5834

Back-transformation

0.0000

0.0000

1.0000

Wald

0.9256

0.0022

0.0722

Third order

0.9507

0.0235

0.0258

200

Central Limit Theorem

0.4936

0.0000

0.5065

Bootstrap (B = 5000)

0.5166

0.0002

0.4834

Back-transformation

0.0000

0.0000

1.0000

Wald

0.9418

0.0120

0.0462

Third order

0.9504

0.0261

0.0235