Abstract:
This thesis investigates diagnostic methods in parametric regression models with
some alternatives to ordinary least squares estimator. Of which, the Liu estimator
has been developed as an alternative to the ordinary least squares estimator in
the presence of collinearity among the regressors in linear regression models.
Firstly, we presented the DFFITS and different versions of the Cook distance
analogous to the ones given for the ordinary linear regression models of each
individual observation on the Liu estimates. We suggested a version of the Cook
distance based on one-step approximation. The mean shift outlier model for the
Liu
regression
has
also
been
investigated.
Moreover,
using
the
Sherman-Morrison-Woodbury theorem, we proposed approximate versions of
the DFFITS and the Cook distance.
Next, the pseudo likelihood function is given for estimating the regression
coefficients and shape parameter as well as to establish local influence
diagnostics.
The normal curvatures of local influence are deduced under
arbitrary perturbation schemes to detect influential observations.
Then, we discussed the assessment of local influence under the modified ridge
regression with normal error distribution. Using a pseudo-likelihood function, we
expressed the normal curvatures of local influence for useful perturbation schemes
in interpretable forms.Finally, local influence diagnostic methods in the modified ridge regression are
deduced under heavy-tailed error distribution.
The methods of analysis we
presented have considerable significance for the detection of influential
observations in the Liu and the modified ridge regression models. Examples
using real-life data sets are used to illustrate the proposed methodology.
