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Title: Robust quantile regression in R Authors:  Christian Eduardo Galarza Morales - Escuela Superior Politecnica del Litoral (Ecuador) [presenting]
Luis Enrique Benites Sanchez - University of Sao Paulo (Brazil)
Victor Hugo Lachos Davila - University of Connecticut (United States)
Abstract: It is well known that the widely popular mean regression model could be inadequate if the probability distribution of the observed responses do not follow a symmetric distribution. To deal with this situation, the quantile regression turns to be a more robust alternative for accommodating outliers and the misspecification of the error distribution since it characterizes the entire conditional distribution of the outcome variable. A likelihood-based approach is presented for the estimation of the regression quantiles based on a new family of skewed distributions. This family includes the skewed version of Normal, Student-t, Laplace, contaminated Normal and slash distribution, all with the zero quantile property for the error term, and with a convenient and novel stochastic representation which facilitates the implementation of the EM algorithm for maximum-likelihood estimation of the $p$th quantile regression parameters. We evaluate the performance of the proposed EM algorithm and the asymptotic properties of the maximum-likelihood estimates through empirical experiments and application to a real life dataset. The algorithm is implemented in the R package \texttt{lqr()}, providing full estimation and inference for the parameters as well as simulation envelopes plots useful for assessing the goodness-of-fit.