Table 3: Comparison in different scales (Skewed-normal).

prev = 0.55, sen = spec = 0.85, ω0 = 0.85, EF = 0.81

Setups

Parameters

True

Empirical

NP Bayes

MLE (EM)

n1 = 50

μ T

3.71

3.7335

3.7068

3.7802

α T ()N(3.52,0.89) μ C

3.23

3.2273

3.2192

3.2242

α C ()N(3.02,0.89)

q

0.48

0.5062

0.5059

0.5560

α = 1

σ C 2

0.35

0.3476

0.3440

0.3214

σ T 2

0.3754

0.3853

0.3751

0.3746

ω 1

0.8738

0.85

0.8918

0.8357

Reject H0

-

0.4391

0.4691

0.4750

n ^ 2 (Med/Mean/Trim)

-

(100,252,116)

(100,202,110)

(100,232,113)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = 4  

3.71

3.7344

3.7076

3.7714

 

3.23

3.2271

3.2190

3.2305

q

0.48

0.5073

0.5070

0.5409

 

0.35

0.3489

0.3452

0.3282

 

0.3754

0.3868

0.3763

0.3775

 

0.8738

0.85

0.8969

0.8701

Reject H0

-

0.4511

0.4810

0.4451

 

-

(100,253,123)

(100,235,116)

(100,251,116)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = 4 μ T

3.71

3.7347

3.7079

3.7528

μ C

3.23

3.2269

3.2188

3.2313

q

0.48

0.5078

0.5075

0.5214

σ C 2

0.35

0.3494

0.3456

0.3322

σ T 2

0.3754

0.3873

0.3768

0.3757

ω 1

0.8738

0.85

0.8986

0.8933

Reject H0

-

0.4511

0.4850

0.4291

n ^ 2 (Med/Mean/Trim)

-

(100,294,126)

(100,199,117)

(100,242,116)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = 10 μ T

3.71

3.7348

3.7080

3.7526

μ C

3.23

3.2268

3.2187

3.2314

q

0.48

0.5080

0.5077

0.5212

σ C 2

0.35

0.3495

0.3457

0.3326

σ T 2

0.3754

0.3875

0.3770

0.3754

ω 1

0.8738

0.85

0.8988

0.8969

Reject H0

-

0.4511

0.4790

0.4271

n ^ 2 (Med/Mean/Trim)

-

(100,301,125)

(100,200,116)

(100,246,116)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = 25 μ T

3.71

3.7331

3.7064

3.7880

μ C

3.23

3.2274

3.2193

3.2207

q

0.48

0.5057

0.5054

0.5674

σ C 2

0.35

0.3468

0.3433

0.3182

σ T 2

0.3754

0.3845

0.3744

0.3731

ω 1

0.8738

0.85

0.8911

0.8193

Reject H0

-

0.4251

0.4711

0.4910

n 2 (Med/Mean/Trim)

-

(100,221,114)

(100,177,109)

(100,221,111)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = -4 μ T

3.71

3.7320

3.7053

3.7908

μ C

3.23

3.2277

3.2196

3.2104

q

0.48

0.5043

0.5041

0.5804

σ C 2

0.35

0.3453

0.3420

0.3133

σ T 2

0.3754

0.3829

0.3730

0.3662

ω 1

0.8738

0.85

0.8901

0.8124

Reject H0

-

0.4052

0.4551

0.5549

n 2 (Med/Mean/Trim)

-

(100,203,111)

(100,212,109)

(100,217,108)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = -10 μ T

3.71

3.7317

3.7050

3.7991

μ C

3.23

3.2277

3.2196

3.2067

q

0.48

0.5040

0.5038

0.5924

σ C 2

0.35

0.3449

0.3416

0.3101

σ T 2

0.3754

0.3825

0.3726

0.3654

ω 1

0.8738

0.85

0.8903

0.8040

Reject H0

-

0.4132

0.4611

0.6008

n 2 (Med/Mean/Trim)

-

(100,195,111)

(100,180,108)

(100,211,109)

n1=50 α T ()N(3.52,0.89) α C ()N(3.02,0.89) α = -25 μ T

3.71

3.7316

3.7049

3.8008

μ C

3.23

3.2277

3.2195

3.2056

q

0.48

0.5039

0.5037

0.5952

σ C 2

0.35

0.3448

0.3415

0.3092

σ T 2

0.3754

0.3824

0.3725

0.3651

ω 1

0.8738

0.85

0.8905

0.8017

Reject H0

-

0.4132

0.4691

0.6048

n 2 (Med/Mean/Trim)

-

(100,194,110)

(100,182,108)

(100,200,109)