(A) stepwise approach for the detection of influential observations in linear regression model

Abstract

In the statistical literature on regression analysis, much attention has been given to problems of detecting observations which, individually or jointly, exert a disproportionate influence on the outcome of linear regression analysis and to problems of assessing the influence of such cases. Most approaches are ways of measuring the change in some feature of analysis on the deletion of one or more observations. Various measures have been proposed which emphasize different aspects of influence on the linear regression. Among them the influence measure, $\mbox{C_m(X(d_m)X(d_m),\;\; ps^2(d_m}$)), proposed by Cook and Weisberg (1982) is mainly treated in this thesis. This measure will be called Cook-Weisberg measure in this thesis. This thesis is written with the intention of fulfilling four needs for Cook-Weisberg measure. First, even though Cook-Weisberg measure was proposed in 1982, an appropriate critical point has not been given. A critical point is suggested for the measure under the normality assumption. Second, an easy computational form of the measure is derived. Third, when computing the measure in practical problem, an efficient computational procedure is proposed. Fourth, programs are implemented which compute the influence measure with the stepwise approach.