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College of Arts & Sciences
Department of Statistics

Karl Gregory Colloquium

Tuesday, February 9, 2016 - 2:45pm

Statistics Department Colloquium

Where: LeConte College, Room 210

Speaker: Karl Gregory

Affiliation: Universität Mannheim, Department of Statistics

Title:  Pointwise inference in the high-dimensional additive model

Abstract: We consider the construction of pointwise confidence intervals for a
single function in the additive nonparametric regression model, in which
the conditional mean of the response is the sum of a large number of
covariate effects of unspecified form.  We allow the number of
covariates to grow along with the sample size while assuming that only a
small but growing number of the covariates have an influence on the
response. Estimation in this setting is well-studied, but there exists
almost no machinery for inference, as estimators typically involve Lasso
penalization and have very complicated distributions.  We introduce an
estimator which is asymptotically normal by adapting ``desparsified
Lasso'' techniques recently introduced in the linear regression setting
to the nonparametric regression setting.  Moreover, we develop a
two-step presmoothing-resmoothing estimator which yields asymptotically
optimal pointwise confidence intervals for a single function in the
sense that our estimator achieves, asymptotically, up to first order
terms, the same bias and variance as the oracle estimator, for which
only the function of interest is unknown.