Permutation-based uncertainty quantification about a mixing distribution

Understand

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem.

• Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing distribution.
• This paper focuses on estimation via the predictive recursion algorithm, and here we take advantage of this estimator's seemingly undesirable dependence on the data ordering to obtain a permutation-based approximation of the sampling distribution which can be used to quantify uncertainty.
• Theoretical and numerical results confirm that the proposed method leads to valid confidence intervals, at least approximately.