Regression diagnostics methods for Liu estimator under the general linear regression model

Abstract

This paper introduces the regression diagnostic methods for the Liu estimator under the general linear regression model with the autocorrelated error structure which is modeled by first-order autoregressive process. To identify the leverage observations, quasi-projection matrix is used, and to identify the influential observations DFFITS and Cook’s D statistics which are single case deletion methods are used for the Liu estimator. For a special model with two explanatory variables, the leverage attitudes of the first observation are examined theoretically according to the autocorrelation coefficient and the Liu parameter. The proposed diagnostic methods are investigated through a numerical example.

Keywords:

• Leverages
• Influence measure
• Liu estimator
• Autocorrelation
• Multicollinearity

Notes

1 The biased estimator introduced by Liu (1993) was first named as ‘Liu Estimator’ by Akdeniz and Kaçiranlar (1995) after Liu’s (1993) paper. To avoid confusion with the Liu estimator under the $E\left(\epsilon {\epsilon }^T\right)={\sigma }_{\epsilon }^2{I}_n,{\widehat{\beta }}^d$ estimator is called as the autocorrelated Liu estimator throughout the paper.

Additional information

Funding

Supported by Çanakkale Onsekiz Mart University Scientific Research Projects Coordination Unit [Project Number: FHD-2018-2620].