Abstract
The use of influence curve as a measure of sensitivity is not new in the literature but has not been properly explored to the best of our knowledge. In particular, the mathematical derivation of the influence function for several popular nonparametric estimators (such as trimmed mean, α-winsorized mean, Pearson product moment correlation coefficient etc. among notable ones) is not given in adequate detail. Moreover, the summary of the final expressions given in some sporadic cases does not appear to be correct. In this article, we aim to examine and summarize the derivation of the influence curve for various well-known estimators for estimating the location of a population, many of which are considered in the nonparametric paradigm.
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