Constrained High Dimensional Statistical Inference

Abstract

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained. However, in many problems, there are natural constraints on model parameters and one is interested in whether the parameters are on the boundary of the constraint or not. e.g. non-negativity constraints for transmission rates in network diffusion. In this paper, we provide algorithms to solve this problem of hypothesis testing in high-dimensional statistical models under constrained parameter space. We show that following our testing procedure we are able to get asymptotic designed Type I error under the null. Numerical experiments demonstrate that our algorithm has greater power than the standard algorithms where the constraints are ignored. We demonstrate the effectiveness of our algorithms on two real datasets where we have emphintrinsic constraint on the parameters.

Publication
arXiv:1911.07319
Ming Yu
Ming Yu
PhD (2016-2020)

Ming received his PhD in Econometrics and Statistics at University of Chicago, Booth School of Business in March 2020. His research interests include high dimensional statistical inference, non-convex optimization, and reinforcement learning, with a focus on developing novel methodologies with both practical applications and theoretical guarantees.

Mladen Kolar
Mladen Kolar
Associate Professor of Econometrics and Statistics

Mladen Kolar is an Associate Professor of Econometrics and Statistics at the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data.

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