Estimating a probability mass function with unknown labels

Abstract

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We prove strong consistency and derive the rates of convergence, for an extended model version of the estimator. We also study a sieved estimator for which similar consistency results are derived. Numerical computation of the sieved estimator is of great interest for practical problems, such as forensic DNA analysis, and we present a computational algorithm based on the stochastic approximation of the expectation maximisation algorithm. As an interesting byproduct of the numerical analyses we introduce an algorithm for bounded isotonic regression for which we also prove convergence.

45 pages (30 page+15 page appendix), v5 corrects a technical problem with the pdf output of v4, otherwise unchanged

References in corpus (2)

• Asymptotic normality of a nonparametric estimator of sample coverage
• Limit properties of the monotone rearrangement for density and regression function estimation

Cited by in corpus (8)

• A nonparametric Bayesian approach to the rare type match problem
• Bayesian approach to LR assessment in case of rare type match: careful derivation and limits
• Impact of model choice on LR assessment in case of rare haplotype match (frequentist approach)
• On the High Accuracy Limitation of Adaptive Property Estimation
• On the Competitive Analysis and High Accuracy Optimality of Profile Maximum Likelihood
• The Broad Optimality of Profile Maximum Likelihood
• Extrapolating the profile of a finite population
• Partial exchangeability of the prior via shuffling