Abstract: Likelihood displacement is a useful measure of influence. Ideally, we would like to have a complete influence graph of the likelihood displacement. As complete graphs cannot be obtained easily in most situations, previous works have considered methods for extracting critical information contained in the graphs. Emphases have been placed on characterizing the graphs at specific points, such as the optimal point or the boundary points. In this paper, we adopt a different perspective and develop measures which describe the total behavior of a likelihood displacement function. Two measures, namely the standardized arc-length and the mean displacement, are constructed and their applications are illustrated with the case-weights linear regression model.
Key words and phrases: Likelihood displacement, linear regression, mean displacement, standardized arc-length, total displacement.