Bodhi Sen is an Associate Professor in the Statistics Department at Columbia University. One of his research interests is nonparametric functional estimation with shape restrictions. He introduces his work by saying,

“Nonparametric function estimation is mostly concerned with understanding the structure (trend/pattern) in the data without making strong parametric assumptions on its form. Most estimation procedures for a nonparametric function (e.g., kernel smoothing), be it a regression function or a probability density, make smoothness assumptions on the underlying function and use local averaging techniques. These estimators depend crucially on tuning parameter(s) (e.g., smoothing bandwidths) and the choice of such parameter(s) can be very problematic.”

His seminar will be held on March 11 at 1:40pm in ETB room 1005; he will also be presenting related work in the Statistics Department on March 10th.

Title: Nonparametric Convex Regression

Abstract: We consider nonparametric least squares estimation of a

convex regression function. We will discuss the characterization,

computation and consistency of the estimator. A computational

framework for multivariate convex regression and some of its variants

— non-decreasing/non-increasing convex regression and Lipschitz

convex regression — will also be presented.

An approach to obtaining smooth convex approximations to the fitted

(piecewise affine) convex least squares estimator, with provide formal

bounds on the quality of approximation, will also be discussed. If

time permits, dimension reduction techniques in this setup will also

be presented.