Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors.
Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors.
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DOI：
10.1080/10618600.2014.899237
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发表时间：
2014-10-01
期刊：
影响因子：
--
通讯作者：
Carroll RJ
中科院分区：
文献类型：
--
作者：
Sarkar A;Mallick BK;Staudenmayer J;Pati D;Carroll RJ
我们考虑的问题，估计密度的一个随机变量时，精确的测量变量是不可用的，但复制代理污染测量误差可用于足够多的科目。在附加测量误差的假设下，这减少到密度的反卷积问题。反卷积方法通常对感兴趣的密度和测量误差的分布做出限制性的和不切实际的假设，例如，正态性和同方差性，因此独立于感兴趣的变量。本文放宽这些假设，并介绍了新的贝叶斯半参数方法的基础上，狄利克雷过程混合模型的强大的反卷积的密度存在条件异方差测量误差。特别是，模型可以适应不对称，重尾和多模态。在模拟实验中，我们表明，我们的方法大大优于最近的贝叶斯方法的基础上估计的密度，通过混合样条。我们将我们的方法应用于营养流行病学数据。即使在测量误差是同方差的特殊情况下，我们的方法是新颖的，并优于其他方法已经提出了以前。额外的模拟结果，获得访问数据集和R程序实现我们的方法的说明包括作为在线补充材料的一部分。
We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, e.g., normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. In particular, the models can adapt to asymmetry, heavy tails and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the data set and R programs implementing our methods are included as part of online supplemental materials.
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影响因子：
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