  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.
