Estimators

n = 10

MLE

BSE

BEN

BCL

$\widehat{\lambda }$

1.033686

1.003013

0.9978051

1.160923

MSE

0.166474

0.07241902

0.07111619

0.072879

L

-6.350954

-4.9385

-13.81305

-10.41417

AIC

15.07691

12.25219

30.00111

23.20334

BIC

15.00449

12.17978

29.92869

23. 13093

n = 30

$\widehat{\lambda }$

0.9816438

0.991284

0.99964

1.005751

MSE

0.039308

0.030747

0.029941

0.030747

L

-13.1564

-15.2890

-24.64788

-13.21051

AIC

28.42004

32.68516

51.40291

28.52816

BIC

29.71409

33.9792

52.6969

29.8222

n = 150

$\widehat{\lambda }$

0.995469

0.998004

0.9965661

1.001133

MSE

0.0069195

0.006578301

0.006535639

0.0065790

L

-79.08826

-75.59041

-105.6675

-81.1737

AIC

160.1765

153.2011

213.3351

164.3474

BIC

163.1871

156.1915

216.3457

167.358

n = 300

$\widehat{\lambda }$

0.9949605

1.013197

0.9936484

0.9942531

MSE

0.003398617

0.0032999

0.003304556

0.003321389

L

-183.2983

-182.7589

-165.4214

-156.1926

AIC

368.5965

367.5179

332.8529

314.3853

BIC

372.3003

317.2217

336.5466

318.0891

n = 1000

$\widehat{\lambda }$

1.001877

1.000891

1.001926

0.9990892

MSE

0.00100733

0.000980377

0.000997429

0.000996724

L

-567.925

-604.1954

-555.8084

-541.6347

AIC

1137.85

1210.389

1113.617

1085.269

BIC

1142.758

1215.297

1118.524

1090.179