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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.