### What's New in the Department

Events
• Hanna Jankowski: The isotonic single index model (Thursday, April 06, 2017)
Time: 3:30pm-4:30pm and Room: WSC 248
Speaker: Hanna Jankowski from York Univ.
Title: The isotonic single index model under fixed and random designs

Abstract:  We study the monotone single index model where a real response variable Y is linked to a multivariate covariate X through the relationship $E[Y|X]=f_0(\alpha_0^TX)$ almost surely. Both the ridge function, $f_0$, and the index parameter, $\alpha_0$, 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 $f_0(\alpha_0^Tx)$ is $n^{1/3}$.   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.

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