Anytime valid and asymptotically optimal inference driven by predictive recursion
arXiv:2309.13441 · doi:10.1093/biomet/asae066
Abstract
Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the stopping rule that determines the data collection process is not available. This paper proposes an e-process construction based on the predictive recursion (PR) algorithm originally designed to recursively fit nonparametric mixture models. The resulting PRe-process affords anytime valid inference and is asymptotically efficient in the sense that its growth rate is first-order optimal relative to PR's mixture model.
Comments welcome at https://researchers.one/articles/23.09.00006
References in corpus (12)
- Misspecification in infinite-dimensional Bayesian statistics
- Time-uniform, nonparametric, nonasymptotic confidence sequences
- Test Martingales, Bayes Factors and -Values
- A nonparametric empirical Bayes framework for large-scale multiple testing
- Consistency of a recursive estimate of mixing distributions
- Stochastic Approximation and Newton's Estimate of a Mixing Distribution
- Semiparametric inference in mixture models with predictive recursion marginal likelihood
- Optimal post-selection inference for sparse signals: a nonparametric empirical-Bayes approach
- A possibility-theoretic solution to Basu's Bayesian--frequentist via media
- On nonparametric estimation of a mixing density via the predictive recursion algorithm
- Revisiting consistency of a recursive estimator of mixing distributions
- A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions