Parametric quantile regression based on the generalized gamma distribution
Parametric quantile regression based on the generalized gamma distribution
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DOI：
10.1111/rssc.12014
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
A. Noufaily;M. C. Jones
中科院分区：
文献类型：
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作者：
A. Noufaily;M. C. Jones
我们探讨了一个特定的完全参数的分位数回归方法，并表明这种方法可以是非常成功的。受提供参考图表的启发，我们在正响应变量的特定背景下工作，其条件分布由广义伽马分布建模，以及单个协变量，广义伽马分布的参数依赖于其通过简单的线性和对数线性形式。最多只有六个参数，这样的模型允许一个可能令人惊讶的广泛的分布形状，似乎足以满足许多实际情况。我们证明了模型的极大似然估计在计算上非常简单，估计的分位数表现良好，使用标准的极大似然渐近法对所需参数的数量进行似然比检验，并基于预期信息矩阵给出逐点置信带，在这种情况下是可靠的，我们更试探性地提供了整个模型的简单拟合优度检验。两个数据分析，从健康和环境领域，包括沿着模拟结果。我们认为，像这样的直接参数最大似然方法-也避免了分位数交叉的问题-对于许多情况来说是足够的，并且在实践中，不需要像人们想象的那样诉诸更复杂的半参数和非参数方法来进行分位数回归。
We explore a particular fully parametric approach to quantile regression and show that this approach can be very successful. Motivated by the provision of reference charts, we work in the specific context of a positive response variable, whose conditional distribution is modelled by the generalized gamma distribution, and a single covariate, the dependence of parameters of the generalized gamma distribution on which is through simple linear and log‐linear forms. With only six parameters at most, such models allow a perhaps surprisingly wide range of distributional shapes that seems adequate for many practical situations. We show that maximum likelihood estimation of the models is computationally quite straightforward, that the estimated quantiles behave well, that use of standard maximum likelihood asymptotics to perform likelihood ratio tests of the number of parameters needed and to give pointwise confidence bands based on the expected information matrix are reliable in this context, and we more tentatively provide a simple goodness‐of‐fit test of the whole model. Two data analyses, from the health and environmental spheres, are included, along with simulation results. We claim that quite a direct parametric maximum likelihood approach like this—which also obviates the problem of quantile crossing—is adequate for many situations, and there is less need than one might think to resort to more complicated semiparametric and non‐parametric approaches to quantile regression in practice.