Quantile Regression Neural Networks: A Bayesian Approach

This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) the response variable. It is shown that posterior feedforward asymptotically consistent under misspecified ALD model. consistency proof embeds problem from density domain and uses bounds on bracketing entropy to derive over Hellinger neighborhoods. result in setting where number of hidden nodes grow with sample size. The implementation utilizes normal-exponential mixture representation density. algorithm Markov chain Monte Carlo (MCMC) simulation technique - Gibbs sampling coupled Metropolis–Hastings algorithm. We have addressed issue complexity associated afore-mentioned MCMC context convergence, choice starting values, step sizes. illustrated proposed studies real data examples.