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Efstathia Bura (TU Vienna)

Sufficient Reductions in Regressions With Exponential Family Inverse Predictors

Venue: Sky Lounge OMP1

Monday, 24.04.2017

The talk will start with a brief introduction and overview of sufficient dimension reduction methodology. The focus will be on a recent paper that appeared in JASA where we develop methodology for identifying and estimating sufficient reductions in regressions with predictors that, given the response, follow a multivariate exponential family distribution. This set-up includes regressions where predictors are all continuous, all categorical or mixtures of categorical and continuous. We derive the minimal sufficient reduction of the predictors and its maximum likelihood estimator by modeling the conditional distribution of the predictors given the response. Whereas nearly all extant estimators of sufficient reductions are linear and only partly capture  the sufficient reduction, our method is not limited to linear reductions. It  also provides the exact form of the sufficient reduction, which is exhaustive, its ML estimates via an  IRLS estimation algorithm, and asymptotic tests for the dimension of the regression.

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Institut für Statistik und Operations Research
University of Vienna

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