On a principal component two-parameter estimator in linear model with autocorrelated errors

This paper is concerned with autocorrelation in errors and multicollinearity among the regressors in linear regression model. To reduce these effects of autocorrelation and multicollinearity, we generalize a principal component two-parameter (PCTP) estimator in the linear regression model with correlated or heteroscedastic errors. Then we give detailed comparisons between those estimators that can be derived from the PCTP estimator such as the generalized least squares estimator, the principal components regression estimator, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$r-k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>r</mi> <mo>-</mo> <mi>k</mi> </mrow> </math> </EquationSource> </InlineEquation> estimator and the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$r-d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>r</mi> <mo>-</mo> <mi>d</mi> </mrow> </math> </EquationSource> </InlineEquation> estimator by the mean squared error (MSE) matrix criterion. Also, we obtain the conditions for the superiority of one estimator over the other. Furthermore, we conduct a Monte Carlo simulation study to compare these estimators under the MSE criterion. Copyright Springer-Verlag Berlin Heidelberg 2015