article · The Annals of Statistics · 2017
Estimating a probability mass function with unknown labels
Dragi Anevski, Richard D. Gill, Stefan Zohren
Cited by 15Open access
Abstract
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.
Cite this paper
Anevski, D., Gill, R. D., & Zohren, S. (2017). Estimating a probability mass function with unknown labels. The Annals of Statistics, 45(6). https://doi.org/10.1214/17-aos1542
Anevski, Dragi, et al. “Estimating a probability mass function with unknown labels.” The Annals of Statistics, vol. 45, no. 6, 2017, https://doi.org/10.1214/17-aos1542.
Anevski, Dragi, Richard D. Gill, and Stefan Zohren. 2017. “Estimating a probability mass function with unknown labels.” The Annals of Statistics 45 (6). https://doi.org/10.1214/17-aos1542.
Anevski, D., Gill, R.D. and Zohren, S. (2017) ‘Estimating a probability mass function with unknown labels’, The Annals of Statistics, 45(6). Available at: https://doi.org/10.1214/17-aos1542.
@article{anevski2017estimating,
title = {{Estimating a probability mass function with unknown labels}},
author = {Anevski, Dragi and Gill, Richard D. and Zohren, Stefan},
journal = {The Annals of Statistics},
volume = {45},
number = {6},
year = {2017},
doi = {10.1214/17-aos1542}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.