Mean and variance estimation in high-dimensional heteroscedastic models with non-convex penalties
Oct 1, 2014·
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0 min read
James Sharpnack
Mladen Kolar
Abstract
Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate heteroscedastic errors, with minor algorithmic modifications (Belloni et al., 2012; Gautier and Tsybakov, 2013). In this work, we study heteroscedastic regression with linear mean model and log-linear variances model with sparse high-dimensional parameters. In this work, we propose estimating variances in a post-Lasso fashion, which is followed by weighted-least squares mean estimation. These steps employ non-convex penalties as in Fan and Li (2001), which allows us to prove oracle properties for both post-Lasso variance and mean parameter estimates. We reinforce our theoretical findings with experiments.
Type
Publication
ArXiv e-prints, arXiv:1410.7874
Authors
Professor of Data Sciences and Operations
Mladen Kolar is a Professor of Data Sciences and Operations at the University of Southern California Marshall School of Business and a Visiting Professor of Statistics and Data Science at Mohamed bin Zayed University of Artificial Intelligence. Before joining USC, he was on the faculty of 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. He is a Fellow of the Institute of Mathematical Statistics.