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....

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.

We consider the problem of selecting grouped variables in linear regression and generalized linear regression models, based on penalized likelihood. A number of penalty functions have been used for this purpose, including the smoothly clipped absolute deviation (SCAD) penalty and the minimax...

An ROC (Receiver Operating Characteristic) curve is a popular tool in the classification of two populations. The nonparametric additive model is used to construct a classifier which is estimated by maximizing the U-statistic type of empirical AUC (Area Under Curve). In particular, the sparsity...

A commonly used semiparametric model is considered. We adopt two difference based estimators of the linear component of the model and propose corresponding thresholding estimators that can be used for variable selection. For each thresholding estimator, variable selection in the linear component...

We consider the squared Euclidean interpoint distances (IDs) among multivariate Bernoulli observations and determine the mean, covariance and the distribution of the IDs within a single group or across two groups. We discuss testing the equality of two distribution functions when the number of...

A selection procedure with no optimization step called LOLA, for Learning Out of Leaders with Adaptation is proposed. LOLA is an auto-driven algorithm with two thresholding steps. The consistency of the LOL procedure (the non adaptive version of LOLA) is proved under sparsity conditions and...