Statistics and Data Science Seminar
Surya Tapas Tokdar
Duke University
Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach
Abstract: I'll introduce a semi-parametric Bayesian framework for a
simultaneous analysis of linear quantile regression models. A simultaneous
analysis is essential to attain the true potential of the quantile regression
framework, but is computationally challenging due to the associated
monotonicity constraint on the quantile curves. For a univariate covariate, we
present a simpler equivalent characterization of the monotonicity constraint
through an interpolation of two monotone curves. The resulting formulation
leads to a tractable likelihood function and is embedded within a Bayesian
framework where the two monotone curves are modeled via logistic
transformations of a smooth Gaussian process. A multivariate extension is
proposed by combining the full support univariate model with a linear
projection of the predictors. The resulting single-index model remains easy to
fit and provides substantial and measurable improvement over the first order
linear heteroscedastic model. I'll provide two illustrative applications to
tropical cyclone intensity and birth weight.
Wednesday November 2, 2011 at 4:00 PM in SEO 636