Statistics and Data Science Seminar
Ivan Mizera
University of Alberta
Quantile tomography: using quantiles with directional data
Abstract: Directional quantile envelopes---essentially, depth contours---are a
possible way to condense the directional quantile information, the
information carried by the quantiles of projections. In typical
circumstances, they allow for relatively faithful and straightforward
retrieval of the directional quantiles, offering a straightforward
probabilistic interpretation in terms of the tangent mass at smooth
boundary points. They can be viewed as a natural, nonparametric
extension of ``multivariate quantiles'' yielded by fitted multivariate
normal distribution, and, as illustrated on data examples, their
construction can be adapted to elaborate frameworks---like estimation
of extreme quantiles, and directional quantile regression---that
require more sophisticated estimation methods than simply evaluating
quantiles for empirical distributions. Their estimates are affine
equivariant whenever the estimators of directional quantiles are
translation and scale equivariant; mathematically, they express the
dual aspect of directional quantiles.
Wednesday October 26, 2011 at 4:00 PM in SEO 636