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....

High dimensional covariance matrix estimation is considered in the context of empirical asset pricing. In order to see the effects of covariance matrix estimation on asset pricing, parameter estimation, model specification test, and misspecification problems are explored. Along with existing...

In the context of classification, it is a common phenomenon that high-dimensional data such as micro-array data consist of only a few informative components. If one uses standard statistical modeling and estimation procedures with entire information, it tends to overfit the data due to noise...

In this note we consider the n×n random matrices whose (i,j)th entry is f(xiTxj), where xi’s are i.i.d. random vectors in RN, and f is a real-valued function. The empirical spectral distributions of these random inner-product kernel matrices are studied in two kinds of high-dimensional...

A mixture of latent trait models with common slope parameters for model-based clustering of high-dimensional binary data, a data type for which few established methods exist, is proposed. Recent work on clustering of binary data, based on a d-dimensional Gaussian latent variable, is extended by...

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...