A general approach to heteroscedastic linear regression
A general approach to heteroscedastic linear regression
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DOI：
10.1007/s11222-006-9013-8
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发表时间：
2007-06-01
影响因子：
2.2
通讯作者：
Nott, David J.
中科院分区：
文献类型：
--
作者：
Leslie, David S.;Kohn, Robert;Nott, David J.
本文提出了线性回归模型的一般处理，其中误差分布是非参数建模的，误差方差可能是异方差的，从而消除了在许多数据集中转换因变量的需要。模型的均值和方差分量可以是参数的，也可以是非参数的，通过变量选择和模型平均来实现简约。一个贝叶斯方法是用于推理与先验的数据为基础，使估计可以自动进行最小的输入由用户。一个狄利克雷过程混合物先验是用来模拟的误差分布nonparametrically，当模型中没有回归，该方法减少到贝叶斯密度估计，我们表明，在这种情况下，估计量相比有利的一个备受推崇的插件密度估计。我们还考虑了一种方法，用于检查完整模型的拟合。该方法被应用到一些模拟和真实的例子，并被证明工作良好。
Our article presents a general treatment of the linear regression model, in which the error distribution is modelled nonparametrically and the error variances may be heteroscedastic, thus eliminating the need to transform the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with parsimony achieved through variable selection and model averaging. A Bayesian approach is used for inference with priors that are data-based so that estimation can be carried out automatically with minimal input by the user. A Dirichlet process mixture prior is used to model the error distribution nonparametrically; when there are no regressors in the model, the method reduces to Bayesian density estimation, and we show that in this case the estimator compares favourably with a well-regarded plug-in density estimator. We also consider a method for checking the fit of the full model. The methodology is applied to a number of simulated and real examples and is shown to work well.