Prediction when fitting simple models to high-dimensional data
This seminar will take place on Zoom
We study linear subset regression in the context of a high-dimensional linear model. Consider y = a + b’z + e with univariate response y and a d-vector of random regressors z, and a submodel where y is regressed on a set of p explanatory variables that are given by x = M’z, for some d x p matrix M. Here, `high-dimensional’ means that the number d of available explanatory variables in the overall model is much larger than the number p of variables in the submodel. In this paper, we present Pinsker-type results for prediction of y given x. In particular, we show that the mean squared prediction error of the best linear predictor of y given x is close to the mean squared prediction error of the corresponding Bayes predictor E[y|x], provided only that p/log(d) is small. We also show that the mean squared prediction error of the (feasible) least-squares predictor computed from n independent observations of (y,x) is close to that of the Bayes predictor, provided only that both p/log(d) and p/n are small. Our results hold uniformly in the regression parameters and over large collections of distributions for the design variables z.

Please sign up for meetings here: docs.google.com/spreadsheets/d/1GRwPBmtpUwstC4fdLZrnxfnARNYHedHykoRZG4Xq2Bo/edit#gid=0
Date: 15 May 2020, 14:15
Venue: Venue to be announced
Speaker: Hannes Leeb (University of Vienna)
Organising department: Department of Economics
Part of: Nuffield Econometrics Seminar
Booking required?: Not required
Audience: Members of the University only
Editor: Melis Clark