Abstract
In linear regression analysis, detecting anomalous observations is an important step for model building process. Various influential measures based on different motivational arguments and designed to measure the influence of observations on different aspects of various regression results are elucidated and critiqued. The presence of influential observations in the data is complicated by the presence of multicollinearity. In this paper, when Liu estimator is used to mitigate the effects of multicollinearity the influence of some observations can be drastically modified. Approximate deletion formulas for the detection of influential points are proposed for Liu estimator. Two real macroeconomic data sets are used to illustrate the methodologies proposed in this paper.
Highlights
The presence of multicollinearity in the regressors seriously affects the parameter estimation and prediction
Many authors [1,2,3] noted that the influential observations on ridge type estimators are different from the corresponding least squares estimate and that multicollinearity can even disguise anomalous data
Walker and Bitch [2] studied the influence of observations in ordinary ridge regression estimator (ORRE) based on case deletion method
Summary
The presence of multicollinearity in the regressors seriously affects the parameter estimation and prediction. Walker and Bitch [2] studied the influence of observations in ordinary ridge regression estimator (ORRE) based on case deletion method. The main aim of this paper is to assess the global influence of observations in the linear Liu estimator using the method of case deletion. This method has been extensively studied and it is very powerful for detecting influential cases because of its intuitive appeal and its direct connection to the sample influence curves. The first Data set is macro impact of foreign direct investment in Sri Lanka This data set contains four regressors and a response variable with 27 observations.
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