First-Order Data Sensitivity Measures with Applications to a Multivariate Signal-Plus-Noise Problem.

摘要

This reprint considers the use of first-order (implicit -function-based) measures of the sensitivity of statistical parameter estimates to certain elements within the data. Although the methods considered are general, the focus is on a maximum likelihood problem in a signal-plus-noise context. We evaluate the accuracy of the measures and give an example of how they will be used in data analysis for a physical system. Such a concern might arise, for example, when certain elements within the set of data are suspected of being anomalies or outliers. The analyst would generally be interested in knowing the effect of these suspect data on the parameter estimates. This paper explores the use of a gradient-based measure of this sensitivity, which is derived from the implicit function theorem. Although the procedure considered here is generic, this paper is primarily an applications paper that focuses on a signal-plus-noise estimation problem. (kr)