73 research outputs found
Sensitivity of principal Hessian direction analysis
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.Comment: Published at http://dx.doi.org/10.1214/07-EJS064 in the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions
In this paper we introduce an influence measure based on second order
expansion of the RV and GCD measures for the comparison between unperturbed and
perturbed eigenvectors of a symmetric matrix estimator. Example estimators are
considered to highlight how this measure compliments recent influence analysis.
Importantly, we also show how a sample based version of this measure can be
used to accurately and efficiently detect influential observations in practice.Comment: Published in at http://dx.doi.org/10.1214/08-EJS201 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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