This article considers a bent-cable quantile regression model that comprises two linear segments but is smoothly jointed by quadratic bend. very flexible to allow the relationship between response variable and covariate of interest change gradually or abruptly across point value in covariate. However, due non-differentiability objective function regression, it challenge estimate unknown paramet...

Quantile regression is a very important tool to explore the relationship between response variable and its covariates. Motivated by mean with LASSO for compositional covariates proposed Lin et al. (Biometrika 101 (4):785–97, 2014), we consider quantile no-penalty penalty function. We develop computational algorithms based on linear programming. Numerical studies indicate that our methods provid...

Abstract Random Forests were introduced as a Machine Learning tool in Breiman (2001) and have since proven to be very popular and powerful for high-dimensional regression and classification. For regression, Random Forests give an accurate approximation of the conditional mean of a response variable. It is shown here that Random Forests provide information about the full conditional distribution...

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. ...