Quantile Regression and L1 Regularization

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Since Quetelet's work in the 19th century, quantitative social science has emphasized the "average man," and conventional statistical methods have sought to estimate the effects of policy interventions on this average man. But such effects are often quite diverse: medical treatments may improve life expectancy, but also impose serious short term risks on some patients; reducing class sizes may improve performance of good students, but not help weaker ones or vice versa. Quantile regression methods have helped to explore these heterogeneous effects. In contrast to least-squares methods that focus exclusively on estimating conditional mean effects, quantile regression methods enable researchers to focus attention on differential effects at various conditional quantiles. These methods have broad applicability throughout science, and have been increasingly employed in biology, medicine, ecology, hydrology, meteorology and other fields as well as in econometrics. Quantile regression is gradually evolving into a comprehensive strategy for the analysis of statistical models focused on estimating slices of the conditional distribution, thereby complementing the exclusive focus on conditional mean models obtained by least-squares based methods. The project proposes work on a variety of new developments of these methods including: model selection, nonparametric inference, time series and survival analysis, and models for multivariate and longitudinal data. Related work on models of unobserved heterogeneity employing empirical Bayes methods and recent developments in shaped constrained nonparametric maximum likelihood methods is also proposed.