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Abstract:
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Quantile regression provides a more comprehensive relationship between a response and covariates of interest compared to mean regression. When the response is subject to censoring, estimating conditional mean requires strong distributional assumptions on the error whereas (most) conditional quantiles can be estimated distribution-free. Although conceptually appealing, quantile regression for censored data is challenging due to computational and theoretical difficulties arising from non-convexity of the objective function involved, especially when the covariates are high-dimensional. We consider a working likelihood based on Powell's objective function and place spike and slab priors on the regression parameters in a Bayesian framework. In spite of the non-convexity and misspecification issues, we show that the posterior distribution is strong selection consistent. We provide a "Skinny Gibbs" algorithm that can be used to sample the posterior distribution with complexity linear in the number of variables and avoids the computational difficulties associated with optimization of the non-convex objective function.
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