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Estimating a probability mass function with unknown labels

Anevski, Dragi LU ; Gill, Richard D. and Zohren, Stefan (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.

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author
organization
publishing date
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
Inst 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
2018-06-17 05:29:57
@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},
  keyword      = {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    = {Inst Mathematical Statistics},
  series       = {Annals of Statistics},
  title        = {Estimating a probability mass function with unknown labels},
  url          = {http://dx.doi.org/10.1214/17-AOS1542},
  volume       = {45},
  year         = {2017},
}