Quantiles play an essential role in modern statistics, as emphasized by the fundamental work of Parzen (1978) and Tukey (1977). Quantile regression was introduced by Koenker and Bassett (1978) as a complement to least squares estimation (LSE) or maximum likelihood estimation (MLE) and leads to far-reaching extensions of ”classical” regression analysis by estimating families of conditional quant...

The finite sample distributions of the regression quantile and of the extreme regression quantile are derived for a broad class of distributions of the model errors, even for the non-i.i.d case. The distributions are analogous to the corresponding distributions in the location model; this again confirms that the regression quantile is a straightforward extension of the sample quantile. As an ap...

Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary (OLS) in situations where the data colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive presence of outliers heavy tailed distributions. In contrast, quantile regression that computes robust estimates. this work, multivariate extended frame...

This article discusses an extension of censored quantile regression to a distributed setting. With the growing availability massive datasets, it is oftentimes arduous task analyze all data with limited computational facilities efficiently. Our proposed method, which attempts overcome this challenge, comprised two key steps, namely: (i) estimation both Kaplan-Meier estimator and model coefficien...