A new approach to influence diagnostics in superpopulations

Abstract

Influence analysis on a model is one of the most studied topics from a frequentist viewpoint. Basically, disturbances are introduced into the model in order to measure the influence that one or a set of observations has on statistical analysis. The most common disturbance pattern is that of the omission of the observations whose influence is to be studied. In our model, we assume that there are only one or a few outliers because they may often be detected by deletion methods associated with regression diagnostics. However, these methods may fail in the presence of multiple outliers. In this case, the forward search can be used to avoid the masking and swamping problems. This article presents a Bayes approach for the influence analysis on a model in finite populations. Particularly, we develop a new approach to the study of influence in prediction theory, based on the given data rather than on the sampling design for data collection. We propose that the influence analysis on the superpopulation normal regression model and a measure based on the conditional bias from a Bayesian viewpoint is analyzed. Forward deletion formulae based on our influence measure can be defined, but this topic is beyond the scope of this article. Finally, we apply our proposed influence measure in a classic example for water contents of soil specimens. Copyright © 2005 John Wiley & Sons, Ltd.