Some aspects of handling explanatory variables in regression models

Improving the Estimation of Coefficients in Linear Regression Models with Some Missing Observations on Some Explanatory Variables

Regression Transformation Diagnostics for Explanatory Variables

Two types of diagnostics are presented for the transformation of explanatory variables in regression. One is based on the likelihood displacement proposed by Cook and Weisberg (1982) for assessing the in uence of individual cases on the maximum likelihood estimate of a transformation parameter. The other is based on the local in uence theory proposed by Cook (1986) for assessing the in uence of...

Linear regression with compositional explanatory variables

Compositional explanatory variables should not be directly used in a linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the isometric logratio (ilr) transformation is used. It turns out that the resulting model is easy to handle, and that parameter estimation can be done like in usual ...

Some methodological aspects of validation of models in nonparametric regression

In this paper we describe some general methods for constructing goodness of t tests in nonparametric regression models. Our main concern is the development of statisticial methodology for the assessment (validation) of speci c parametric modelsM as they arise in various elds of applications. The fundamental idea which underlies all these methods is the investigation of certain goodness of t sta...

Dimension Reduction of the Explanatory Variables in Multiple Linear Regression

In classical multiple linear regression analysis problems will occur if the regressors are either multicollinear or if the number of regressors is larger than the number of observations. In this note a new method is introduced which constructs orthogonal predictor variables in a way to have a maximal correlation with the dependent variable. The predictor variables are linear combinations of the...