It is shown that the basic regularization procedures for finding meaningful approximate
solutions of ill-conditioned or singular linear systems can be phrased and analyzed in terms …

Although nonparametric regression has traditionally focused on the estimation of conditional
mean functions, nonparametric estimation of conditional quantile functions is often of …

Ultra-high dimensional data often display heterogeneity due to either heteroscedastic
variance or other forms of non-location-scale covariate effects. To accommodate …

Quantile regression is a powerful tool for learning the relationship between a response
variable and a multivariate predictor while exploring heterogeneous effects. This paper …

Abstract ℓ 1-penalized quantile regression (QR) is widely used for analysing high-
dimensional data with heterogeneity. It is now recognized that the ℓ 1-penalty introduces …

In statistical analyses the complexity of a chosen model is often related to the size of
available data. One important question is whether the asymptotic distribution of the …

We obtain strong Bahadur representations for a general class of M-estimators that satisfies
$\Sigma_i\psi (x_i,\theta)= o (\delta_n) $, where the $ x_i $'s are independent but not …

This paper considers a linear triangular simultaneous equations model with conditional
quantile restrictions. The paper adjusts for endogeneity by adopting a control function …

Sparse penalized quantile regression is a useful tool for variable selection, robust
estimation, and heteroscedasticity detection in high-dimensional data analysis. The …

A broad and unified methodology for robust statistics—with exciting new applications Robust
statistics is one of the fastest growing fields in contemporary statistics. It is also one of the …