A skew‐t quantile regression for censored and missing data

Abstract

Quantile regression has emerged as an important analytical alternative to the classical mean regression model. However, the analysis could be complicated by the presence of censored measurements due to a detection limit of equipment in combination with unavoidable missing values arising when, for instance, a researcher is simply unable to collect an observation. Another complication arises when measures depart significantly from normality, for instance, in the presence of skew heavy‐tailed observations. For such data structures, we propose a robust quantile regression for censored and/or missing responses based on the skew‐t distribution. A computationally feasible EM‐based procedure is developed to carry out the maximum likelihood estimation within such a general framework. Moreover, the asymptotic standard errors of the model parameters are explicitly obtained via the information‐based method. We illustrate our methodology by using simulated data and two real data sets.