Quantile regression investigates the conditional quantile functions of a response variables in terms of a set of covariates. Mquantile regression extends this idea by a “quantile-like” generalization of regression based on influence functions. In this work we extend it to nonparametric regression, in the sense that the M-quantile regression functions do not have to be assumed to be linear, but ...

We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In addition, the sparsity consideration in quantile regression enables the exploration of the entire conditional distribution of the response variable given the ...

We introduce a general approach to nonlinear quantile regression modelling that is based on the specification of the copula function that defines the dependency structure between the variables of interest. Hence we extend Koenker and Bassett’s [1978] original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X a...

Abstract. In this article, we derive the asymptotic distribution of the bootstrapped Lasso estimator of the regression parameter in a multiple linear regression model. It is shown that under some mild regularity conditions on the design vectors and the regularization parameter, the bootstrap approximation converges weakly to a random measure. The convergence result rigorously establishes a prev...

INTRODUCTION The Uniform Data Set (UDS) contains neuropsychological test scores and demographic information for participants at Alzheimer's disease centers across the United States funded by the National Institute on Aging. Mean regression analysis of neuropsychological tests has been proposed to detect cognitive decline, but the approach requires stringent assumptions. METHODS We propose usi...

This article introduces regression quantile models using both RS and FKML generalised lambda distributions (GLD) and demonstrates the versatility of proposed models for a range of linear/non linear and heteroscedastic/homoscedastic empirical data. Owing to the rich shapes of GLDs, GLD quantile regression is a competitive flexible model compared to standard quantile regression. The proposed meth...

The present study aims at investigating the relationship between firm specific risk and stock return using cross-sectional quantile regression. In order to study the power of firm specific risk in explaining cross-sectional return, a combination of Fama-Macbeth (1973) model and quantile regression is used. To this aim, a sample of 270 firms listed in Tehran Stock Exchange during 1999-2010 was i...

Testing for Granger non-causality over varying quantile levels could be used to measure and infer dynamic linkages, enabling the identification of quantiles for which causality is relevant, or not. However, dynamic quantiles in financial application settings are clearly affected by heteroscedasticity, as well as the exogenous and endogenous variables under consideration. GARCH-type dynamics are...

Analyses of childhood stunting have mainly used mean regression yet modeling using quantile regression is more appropriate than using mean regression in that the former provides flexibility to analyze the determinants of stunting corresponding to quantiles of interest whereas the latter allows only analyzing the determinants of mean stunting. Bayesian structured additive quantile regression mod...

Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2012) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric l2 adjustment of the loss function around zero. We ext...