Statistics Department Seminar Series: Hanna K. Jankowski, Associate Professor, Department of Mathematics and Statistics, York University

Abstract

We study the monotone single index model where a real response variable Y is linked to a multivariate covariate X through the relationship E[Y |X] = f0(α0T X) almost surely. Both the ridge function, f0, and the index parameter, α0, are unknown and the ridge function is assumed to be monotone. Under random design, we show that the rate of convergence of the estimator of the bundled function f0(α0T x) is n1/3. Furthermore, we show that the least squares estimator is nearly parametrically rate-adaptive to piecewise constant ridge functions. For the fixed design setting, we show that the rate of convergence is parametric, as expected. The latter results are applied to the analysis of several data sets.