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Abstract:
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In this article, we propose new Bayesian methods for selecting and estimating a sparse coefficient vector for skewed heteroscedastic response. Our novel Bayesian procedures effectively estimate median and other quantile functions, assure non-local prior for regression effects in some cases, deal with some observations with large errors, and asymptotically select the true set of predictors even when the number of covariates increases in the same order of the sample size. Via simulation studies and a re-analysis of a medical cost study with large number of potential predictors, we illustrate the ease of implementation and other practical advantages of our approach compared to existing methods for such studies.
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