Estimation of influence functions
The influence function of an estimator is used for mainly two purposes: to indicate the sensitivity of the estimator to particular values and for computing the asymptotic variance of the estimator. Empirical versions of the influence function have been used to indicate influential data points in a particular sample and for constructing variance estimators. In this article influence functions for L-estimators (i.e. linear combinations of order statistics) are considered. In particular, weak approximation theorems for an empirical influence function and for its bootstrapped version are proved. Further, it is indicated how the latter can be used to derive asymptotic confidence bounds for the unknown influence function. Finally, the authors point out that the presented method for treating influence function estimates of L-estimators also works for other estimators such as M- and R-estimators and for U-statistics.
scientific article; zbMATH DE number 3990622