Locally adaptive semiparametric estimation of the mean and variance functions in regression models
Locally adaptive semiparametric estimation of the mean and variance functions in regression models
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DOI：
10.1198/106186006x157441
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发表时间：
2006-12-01
影响因子：
2.4
通讯作者：
Kirby, Chris
中科院分区：
文献类型：
--
作者：
Chan, David;Kohn, Robert;Kirby, Chris
本文提出了一种估计具有高斯误差的异方差回归模型的贝叶斯方法，其中均值和对数方差被建模为解释变量的线性组合。我们使用贝叶斯变量选择先验和模型平均来提高估计的效率。通过将协变量效应表示为基函数的线性组合，允许解释变量灵活地输入均值和对数方差，从而使模型成为半参数模型。我们估计弹性效应的方法是局部自适应的，因为当弹性效应在预测器空间的某些部分变化很快，但在其他部分变化很慢时，它工作得很好。本文提出了一种从后验分布中抽样的马尔可夫链蒙特卡罗模拟方法，并将该方法应用于大量的模拟和实际例子。
This article proposes a Bayesian method for estimating a heteroscedastic regression model with Gaussian errors, where the mean and the log variance are modeled as linear combinations of explanatory variables. We use Bayesian variable selection priors and model averaging to make the estimation more efficient. The model is made semiparametric by allowing explanatory variables to enter the mean and log variance flexibly by representing a covariate effect as a linear combination of basis functions. Our methodology for estimating flexible effects is locally adaptive in the sense that it works well when the flexible effects vary rapidly in some parts of the predictor space but only slowly in other parts. Our article develops an efficient Markov chain Monte Carlo simulation method to sample from the posterior distribution and applies the methodology to a number of simulated and real examples.