Recent Advance in Sensitivity Analysis in Multivariate Statistical Methods

Abstract

Methodologies have been developed in the last two decades for detecting influential observations and evaluating the stability of the results of analysis not only in regression and related methods but also in other multivariate methods. In developing these methodologies influence functions play important roles. The present paper shows that influence functions can be derived in various multivariate statistical methods and that a general strategy based on influence functions and its robust version are useful for detecting singly and/or jointly influential observations. Cases of principal component analysis, exploratory factor analysis and confirmatory factor analysis are studied with numerical examples.

Assessing local influence for specific restricted likelihood: Application to factor analysis

“…Thus, this special scheme is equivalent to the EIC approach. This relationship is also discussed by Tanaka (1994) under a similar context.…”

Evaluation of a pointwise local visual pattern exploration method

“…Sensitivity analysis has been studied in the scope of multivariate data analysis [6] . Sensitivity analysis is the analysis of the variation of the output from a model based on small changes in their inputs.…”

Pointwise local pattern exploration for sensitivity analysis

“…The advantage is that our new system allows users to interactively adjust the local model based on their prior knowledge and the expected model. Sensitivity analysis has been studied in the scope of multivariate data analysis [25]. Sensitivity analysis is the analysis of the variation of the output in a model based on small changes of their inputs.…”