The Annals of Statistics
- Ann. Statist.
- Volume 45, Number 6 (2017), 2708-2735.
Estimating a probability mass function with unknown labels
In the context of a species sampling problem, we discuss a nonparametric 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.
Ann. Statist., Volume 45, Number 6 (2017), 2708-2735.
Received: May 2016
First available in Project Euclid: 15 December 2017
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Anevski, Dragi; Gill, Richard D.; Zohren, Stefan. Estimating a probability mass function with unknown labels. Ann. Statist. 45 (2017), no. 6, 2708--2735. doi:10.1214/17-AOS1542. https://projecteuclid.org/euclid.aos/1513328588
- Supplement to “Estimating a probability mass function with unknown labels”. Supplement consisted of Supplement A: Existence of the PML; Supplement B: Computation of the PML, and Supplement C: An algorithm for estimating a decreasing multinomial probability with lower bound.