Quantile regression has important applications in risk management, portfolio optimization, and asset pricing. The current paper studies estimation, inference and …nancial applications of quantile regression with cointegrated time series. In addition, a new cointegration model with varying coe¢ cients is proposed. In the proposed model, the value of cointegrating coe¢ cients may be a¤ected by th...

The worm plot is a series of detrended Q-Q plots, split by covariate levels. The worm plot is a diagnostic tool for visualizing how well a statistical model fits the data, for finding locations at which the fit can be improved, and for comparing the fit of different models. This paper shows how the worm plot can be used in conjunction with quantile regression. No parametric distributional assum...

Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in...

In this comment, we offer a nontechnical discussion of conventional (conditional) multivariate quantile regression, with an emphasis on the appropriate interpretation of results. We discuss its distinction from unconditional quantile regression, an analytic method that can be used to estimate varying associations between predictors and outcome at different points of the outcome distribution. We...

Tropospheric ozone is one of the six criteria pollutants regulated by the United States Environmental Protection Agency under the Clean Air Act and has been linked with several adverse health effects, including mortality. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ...

Conditional quantile curves provide a comprehensive picture of a response contingent on explanatory variables. Quantile regression is a technique to estimate such curves. In a flexible modeling framework, a specific form of the quantile is not a priori fixed. Indeed, the majority of applications do not per se require specific functional forms. This motivates a local parametric rather than a glo...

Classical regression methods have focused mainly on estimating conditional mean functions. In recent years, however, quantile regression has emerged as a comprehensive approach to the statistical analysis of response models. In this article we consider the L1-norm (LASSO) regularized quantile regression (L1-norm QR), which uses the sum of the absolute values of the coefficients as the penalty. ...

Statistical Science) Bayesian Spatial Quantile Regression by Kristian Lum Department of Statistical Science Duke University

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically, it obtains the large sample properties of extremal (extr...

This paper is a study of the application of Bayesian Exponentially Tilted Empirical Likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys’ method. For regression quantiles we derive the asymptotic form of the posterior density. We also exami...