English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present methodology for constructing pointwise confidence intervals forthe cumulative distribution function and the quantiles of mixing distributionson the unit interval from binomial mixture distribution samples. No assumptionsare made on the shape of the mixing distribution. The confidence intervals areconstructed by inverting exact tests of composite null hypotheses regarding themixing distribution. Our method may be applied to any deconvolution approachthat produces test statistics whose distribution is stochastically monotone forstochastic increase of the mixing distribution. We propose a hierarchical Bayesapproach, which uses finite Polya Trees for modelling the mixing distribution,that provides stable and accurate deconvolution estimates without the need foradditional tuning parameters. Our main technical result establishes thestochastic monotonicity property of the test statistics produced by thehierarchical Bayes approach. Leveraging the need for the stochasticmonotonicity property, we explicitly derive the smallest asymptotic confidenceintervals that may be constructed using our methodology. Raising the questionwhether it is possible to construct smaller confidence intervals for the mixingdistribution without making parametric assumptions on its shape.

Exact confidence intervals for the mixing distribution from binomial mixture distribution samples