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In this paper, we consider Bayesian methods for non-parametric quantileregressions with multiple continuous predictors ranging values in the unitinterval. In the first method, the quantile function is assumed to be smoothover the explanatory variable and is expanded in tensor product of B-splinebasis functions. While in the second method, the distribution function isassumed to be smooth over the explanatory variable and is expanded in tensorproduct of B-spline basis functions. Unlike other existing methods ofnon-parametric quantile regressions, the proposed methods estimate the wholequantile function instead of estimating on a grid of quantiles. Priors on theB-spline coefficients are put in such a way that the monotonicity of theestimated quantile levels are maintained unlike local polynomial quantileregression methods. The proposed methods have also been modified for quantilegrid data where only the percentile range of each response observations areknown. Simulations studies have been provided for both complete and quantilegrid data. The proposed method has been used to estimate the quantiles of UShousehold income data and North Atlantic hurricane intensity data.

Bayesian Non-parametric Simultaneous Quantile Regression for Complete and Grid Data