Biased estimators and diagnostic methods in general linear statistical model

Regression diagnostics methods have been often studied for determination of leverage/influential observations under the linear statistical model with uncorrelated and homoscedastic errors. However, the errors of the model may not be always uncorrelated and homoscedastic in real applications. This research includes regression diagnostics methods in the linear statistical model with correlated errors and correlated regressors. The correlation between the error terms is modeled by first order autoregressive process. Regression diagnostics methods have been studied theoretically by using generalized least square and ridge regression estimators. Leverage observation is determined by projection/quasi-projection matrix, influential observation on the regression coefficients is determined by DFBETA, on the response vector is determined by DFFITS, on the regression curve is determined by Cook distance, on the confidence ellipsoid is determined by Cook-Weisberg and Andrews-Pregibon, on the variance-covariance matrix of the regression parameters are determined by COVRATIO. Model validation is examined by OCV, GCV and Cp statistics. In addition to the theoretical investigations, a common numerical example and Monte Carlo simulation study for each topic have been performed.