Bayesian non-parametric simultaneous quantile regression for complete and grid data
Bayesian non-parametric simultaneous quantile regression for complete and grid data
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DOI：
10.1016/j.csda.2018.04.0
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
Priyam Das;S. Ghosal
中科院分区：
文献类型：
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作者：
Priyam Das;S. Ghosal
贝叶斯方法的非参数分位数回归已被认为是多个连续的预测范围内的单位区间的值。基于假设分位函数或分布函数在解释变量中是光滑的，并以B样条基函数的张量积展开，提出了两种方法。与其他现有的非参数分位数回归方法不同，所提出的方法估计整个分位数函数，而不是估计分位数的网格。先验的B样条展开的系数放在这样一种方式，估计的分位数水平的单调性保持不同于本地多项式分位数回归方法。所提出的方法也被修改为分位数网格数据，其中只有百分位数范围的每个响应观测是已知的。所提出的方法和其他一些现有的方法的性能的比较模拟研究提供的预测均方误差和平均L1误差的四分位数。所提出的方法被用来估计美国家庭收入数据和北大西洋飓风强度数据的分位数。
Bayesian methods for non-parametric quantile regression have been considered with multiple continuous predictors ranging values in the unit interval. Two methods are proposed based on assuming that either the quantile function or the distribution function is smooth in the explanatory variables and is expanded in tensor product of B-spline basis functions. Unlike other existing methods of non-parametric quantile regressions, the proposed methods estimate the whole quantile function instead of estimating on a grid of quantiles. Priors on the coefficients of the B-spline expansion are put in such a way that the monotonicity of the estimated quantile levels are maintained unlike local polynomial quantile regression methods. The proposed methods are also modified for quantile grid data where only the percentile range of each response observations are known. A comparative simulation study of the performances of the proposed methods and some other existing methods are provided in terms of prediction mean squared errors and mean L 1-errors over the quartiles. The proposed methods are used to estimate the quantiles of US household income data and North Atlantic hurricane intensity data.