We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually straightforward yet fundamentally novel and highly robust approach to multivariate density deconvolution by stochastically rotating the replicates toward the corresponding true latent values. We also address the additionally significantly challenging problem of accommodating conditionally heteroscedastic measurement errors in this newly introduced framework. We take a Bayesian route to estimation and inference, implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of our analysis. Asymptotic convergence guarantees for the method are also established. We illustrate the method's empirical efficacy through simulation experiments and its practical utility in estimating the long-term joint average intakes of different dietary components from their measurement error contaminated 24-hour dietary recalls.

翻译：我们考虑了多变量密度分解的问题,其中随机矢量的分布需要从被有条件的杂交测量误差污染的复制物中估算出来。我们提出了一个概念上直截了当的、根本上是新颖的和高度有力的方法,通过将复制物转成相应的真实潜值,处理多变量密度分解的问题。我们还解决了在新引入的这一框架中兼顾有条件的杂交测量误差这一具有极大挑战性的问题。我们采取巴伊西亚路线,通过高效的马尔科夫链子蒙特卡洛算法进行估算和推断,适当适应我们分析的所有方面的不确定性。还确立了该方法的安非他命趋同保证。我们通过模拟实验及其在估计测量误差中不同膳食成分的长期平均摄入量方面的实用性,我们通过模拟实验及其在24小时饮食回顾中被污染的计算误差来说明该方法的经验效果。