Table 3: Estimated MSE for OLS, ORR, Liu, KL and the proposed NB.

ρ=0.90, n=50

Eigenvalues of X'X are: 273.8443, 18.5471, and 14.8552

CN of X'X is 4.2935

VIFs are: 4.2216, 3.9332, and 4.7453

σ k=d

OLS

ORR

Liu

KL

NB

1

0.1

0.107464

0.106353

0.098172

0.105242

0.105141

 

0.2

 

0.105242

0.099182

0.103121

0.102616

 

0.3

 

0.104232

0.100192

0.101000

0.099990

 

0.4

 

0.103121

0.101202

0.098879

0.097162

 

0.5

 

0.102111

0.102212

0.096859

0.094233

 

0.6

 

0.101101

0.103323

0.094839

0.091203

 

0.7

 

0.100091

0.104333

0.092920

0.088072

 

0.8

 

0.099081

0.105343

0.091001

0.084840

 

0.9

 

0.098071

0.106454

0.089082

0.081507

5

0.1

2.687711

2.659734

2.452785

2.631858

2.629131

 

0.2

 

2.632161

2.478338

2.577318

2.566410

 

0.3

 

2.605093

2.503992

2.523889

2.499851

 

0.4

 

2.57853

2.529848

2.471672

2.429656

 

0.5

 

2.55227

2.555805

2.420566

2.356128

 

0.6

 

2.526515

2.581863

2.370571

2.27957

 

0.7

 

2.501063

2.608123

2.321586

2.200184

 

0.8

 

2.476116

2.634484

2.273712

2.118374

 

0.9

 

2.451573

2.661047

2.226848

2.034443

10

0.1

10.75074

10.63884

9.810837

10.52753

10.51642

 

0.2

 

10.52875

9.913049

10.30917

10.26554

 

0.3

 

10.42037

10.01587

10.09556

9.999101

 

0.4

 

10.31392

10.11909

9.886587

9.718321

 

0.5

 

10.20908

10.22302

9.682062

9.424209

 

0.6

 

10.10586

10.32745

9.482082

9.117775

 

0.7

 

10.00435

10.43239

9.286243

8.800433

 

0.8

 

9.904464

10.53794

9.094646

8.473193

 

0.9

 

9.80609

10.64409

8.90719

8.137267

Note: Smaller MSE value is bolded in each case.