In this paper, the cross-validation methods namely the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$C_{p}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>C</mi> <mi>p</mi> </msub> </math> </EquationSource> </InlineEquation>, PRESS and GCV are presented under the multiple linear regression model when multicollinearity exists and additional information imposes restrictions among the parameters that should hold in exact terms. The selection...</equationsource></equationsource></inlineequation>

In this study a new two-parameter estimator which includes the ordinary least squares, the principal components regression (PCR) and the Liu-type estimator is proposed. Conditions for the superiority of this new estimator over the PCR, r–k class estimator and Liu-type estimator are derived....

In this paper, an improved ridge type estimator is introduced to overcome the effect of multi-collinearity in logistic regression. The proposed estimator is called a modified almost unbiased ridge logistic estimator. It is obtained by combining the ridge estimator and the almost unbiased ridge...

In this paper, an improved ridge type estimator is introduced to overcome the effect of multi-collinearity in logistic regression. The proposed estimator is called a modified almost unbiased ridge logistic estimator. It is obtained by combining the ridge estimator and the almost unbiased ridge...

We give a new consistency proof for high-dimensional quantile regression estimators. A consequence of this proof is that the number of significant regressors can grow at a rate slog2(s)=o(n). To our best knowledge, this is the fastest rate achieved for high-dimensional quantile regression.