Table 14 Coefficients and MSEs of Estimators for the Australian Institute of Sports Data.

From: Development of the generalized ridge estimator for the Poisson-Inverse Gaussian regression model with multicollinearity

Estimates

Parameters

\(\beta _0\)

\(\beta _1\)

\(\beta _2\)

\(\beta _3\)

\(\beta _4\)

\(\beta _5\)

\(\beta _6\)

\(\beta _7\)

\(\beta _8\)

\(\beta _9\)

\(\beta _{10}\)

MSE

PIGMLE

–

8.4170

0.0652

− 0.0352

− 0.0224

− 0.0534

0.0115

0.0224

0.0164

− 0.0392

0.1340

− 0.0269

103.5890

PIGRRE

\(\hat{k}_1\)

5.9212

0.0651

−  0.0213

− 0.0395

0.0022

0.0113

0.0239

0.0163

− 0.0394

0.1337

− 0.0266

57.6193

\(\hat{k}_2\)

3.4255

0.0650

− 0.0074

− 0.0566

0.0579

0.0111

0.0254

0.0161

− 0.0395

0.1334

− 0.0263

42.2953

\(\hat{k}_3\)

3.4269

0.0650

− 0.0074

− 0.0566

0.0578

0.0111

0.0254

0.0161

− 0.0395

0.1334

− 0.0263

42.2953

\(\hat{k}_4\)

0.0040

0.0309

0.0120

− 0.0462

0.1160

0.0086

0.0033

0.0130

0.0014

0.0434

− 0.0367

70.8322

\(\hat{k}_5\)

9.53e−05

0.0055

0.0157

0.0058

0.0021

0.0032

0.0005

0.0007

0.0042

0.0015

0.0006

70.8747

PIGGRE

\(\hat{K}_1\)

0.0006

0.0007

0.0053

0.0029

7.6e−06

0.0055

0.0083

0.0031

0.0640

0.0053

− 0.0174

42.0372

\(\hat{K}_2\)

0.0020

0.0020

0.0079

− 0.0005

2.97e−05

0.0077

0.0031

0.0075

0.0529

0.0177

− 0.0296

59.7067

\(\hat{K}_3\)

0.0068

0.0066

0.0091

− 0.0057

0.0001

0.0086

− 0.0078

0.0125

0.0365

0.0563

− 0.0314

86.2329

\(\hat{K}_4\)

0.0008

0.0008

0.0060

0.0021

1.02e−05

0.0061

0.0075

0.0039

0.0618

0.0068

− 0.0208

42.9759

\(\hat{K}_5\)

0.0078

0.0200

0.0090

− 0.0183

0.0065

0.0090

0.0008

0.0130

0.0329

0.0529

− 0.0257

67.0565

  1. Bolded values indicate the best biasing parameter.