Estimating a probability mass function with unknown labels
(2017) In Annals of Statistics 45(6). p.2708-2735- 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... (More)
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.
(Less)
- author
- Anevski, Dragi LU ; Gill, Richard D. and Zohren, Stefan
- organization
- publishing date
- 2017-12-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- High profile, Monotone rearrangement, Nonparametric, NPMLE, Ordered, Probability mass function, Rates, SA-EM, Sieve, Strong consistency
- in
- Annals of Statistics
- volume
- 45
- issue
- 6
- pages
- 28 pages
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- scopus:85040173964
- wos:000418371600015
- ISSN
- 0090-5364
- DOI
- 10.1214/17-AOS1542
- language
- English
- LU publication?
- yes
- id
- f8894c8e-5f03-45ed-9c21-013ce0a17dcc
- date added to LUP
- 2018-01-15 10:25:11
- date last changed
- 2024-02-13 13:43:13
@article{f8894c8e-5f03-45ed-9c21-013ce0a17dcc,
abstract = {{<p>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.</p>}},
author = {{Anevski, Dragi and Gill, Richard D. and Zohren, Stefan}},
issn = {{0090-5364}},
keywords = {{High profile; Monotone rearrangement; Nonparametric; NPMLE; Ordered; Probability mass function; Rates; SA-EM; Sieve; Strong consistency}},
language = {{eng}},
month = {{12}},
number = {{6}},
pages = {{2708--2735}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Annals of Statistics}},
title = {{Estimating a probability mass function with unknown labels}},
url = {{http://dx.doi.org/10.1214/17-AOS1542}},
doi = {{10.1214/17-AOS1542}},
volume = {{45}},
year = {{2017}},
}