Date/Time
Date(s) - 19/11/2024
3:30 pm - 4:30 pm

Location: MDCL 3020

Speaker: Hanna Jankowski (York University)

Title: The isotonic single index model under fixed and random designs

Abstract: To quote L. Wasserman, probability theory asks “Given a data generation process, what are the properties of the outcomes?”, while statistics ask “Given the outcomes, what can we say about the process that generated the data?”, where the latter question can be viewed as solving an inverse problem.  I will begin the talk by motivating shape-constrained methods of estimation in the context of solving the inverse problem while striking a balance between robustness (bias) and efficiency (variance), the two key sources of error in statistical estimation. I will then discuss some recent results on the monotone single index model, a dimension reduction model. This is joint work with Fadoua Balabdaoui (ETHZ) and Cecile Durot (Paris X).  In the monotone single index model a real response variable $Y$ is linked to a multivariate covariate $X$ through its mean via $E[Y|X=x]=f(\alpha^Tx)$.  Both the ridge function $f$ and index $\alpha$ are assumed unknown and we assume that the ridge function is monotone.  Under random design, we show that the rate of convergence of the mean estimator is $n^{-1/3},$ whereas under fixed design, the rate of convergence is parametric, as expected.