Sensitivity of principal Hessian direction analysis

TL;DR

This paper compares the sensitivity of two versions of principal Hessian directions (pHd) for dimension reduction, analyzing how small data perturbations and outliers influence their estimation and practical detection of influential observations.

Contribution

It provides a detailed sensitivity analysis of two pHd methods and explores their differing behaviors and robustness to outliers using influence functions.

Findings

Two pHd versions can behave very differently under certain data conditions.

Outliers may or may not be highly influential in practice.

Influence functions can effectively detect influential observations.

Abstract

We provide sensitivity comparisons for two competing versions of the dimension reduction method principal Hessian directions (pHd). These comparisons consider the effects of small perturbations on the estimation of the dimension reduction subspace via the influence function. We show that the two versions of pHd can behave completely differently in the presence of certain observational types. Our results also provide evidence that outliers in the traditional sense may or may not be highly influential in practice. Since influential observations may lurk within otherwise typical data, we consider the influence function in the empirical setting for the efficient detection of influential observations in practice.