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Theoretical and numerical aspects of the pattern maximum likelihood estimator, with a view towards symmetric functionals estimation

Benthem Ciano, Paulina LU (2022) In Bachelor's Theses in Mathematicas Sciences MASK11 20221
Mathematical Statistics
Abstract
Suppose that an infinite population is partitioned into different species. Given a random sample from the population of species, we are interested in estimating the species richness, which is the number of different species inhabiting a given area.
The species richness is a symmetric functional of the probability mass function. A suitable model for estimating the probability mass function is via the pattern maximum likelihood.
When the pattern maximum likelihood cannot be found analytically,
a sieved version of the pattern maximum likelihood can be used to find a numerical solution to the likelihood problem. The sieved pattern maximum likelihood estimator is consistent and can be calculated numerically using the SAEM algorithm.
Please use this url to cite or link to this publication:
author
Benthem Ciano, Paulina LU
supervisor
organization
course
MASK11 20221
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor's Theses in Mathematicas Sciences
report number
LUNFMS-4065-2022
ISSN
1654-6229
other publication id
2022:K12
language
English
id
9091178
date added to LUP
2022-06-27 10:24:16
date last changed
2022-06-30 14:14:51
@misc{9091178,
  abstract     = {{Suppose that an infinite population is partitioned into different species. Given a random sample from the population of species, we are interested in estimating the species richness, which is the number of different species inhabiting a given area. 
The species richness is a symmetric functional of the probability mass function. A suitable model for estimating the probability mass function is via the pattern maximum likelihood.
When the pattern maximum likelihood cannot be found analytically, 
a sieved version of the pattern maximum likelihood can be used to find a numerical solution to the likelihood problem. The sieved pattern maximum likelihood estimator is consistent and can be calculated numerically using the SAEM algorithm.}},
  author       = {{Benthem Ciano, Paulina}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematicas Sciences}},
  title        = {{Theoretical and numerical aspects of the pattern maximum likelihood estimator, with a view towards symmetric functionals estimation}},
  year         = {{2022}},
}