Influence diagnostics for fractional principal components estimators in regression

Fractional Principal Components (FPC) is a large class of estimators that include, among others, least squares (LS), ridge and generalized ridge, principal components, fractional rank, and Stein estimators (see Hocking, et. al 1976). The object of this paper is to analyze the influence of single observations and propose diagnostics for this class of estimators. Approximate deletion formulas are obtained and their agreement with the "true" influence analyzed. These diagnostics are illustrated using two examples.