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Maximum likelihood estimation of a monotone probability mass function with unknown labels

Greselin, Pietro (2019) In Master's Theses in Mathematical Sciences FMSM01 20191
Mathematical Statistics
Abstract
In this paper we discuss methods to estimate a monotone frequency of species
in a population when the ordering of species is unknown.
The question arises from [5], where the case of known order was taken
into account, and the method is inspired by [2].
We discuss first a regression approach that however only leads to the
trivial solution, and then a likelihood approach that allows some generali-
sations and provides inspiration for future work. We discuss existence and
uniqueness of the solution, and future work might be related to discussing
consistency as well as asymptotic distribution results and if possible to look
for an analytic expression of it.
Please use this url to cite or link to this publication:
author
Greselin, Pietro
supervisor
organization
course
FMSM01 20191
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3372-2019
ISSN
1404-6342
other publication id
2019:38
language
English
id
8984708
date added to LUP
2019-06-17 11:45:04
date last changed
2024-09-30 12:35:17
@misc{8984708,
  abstract     = {{In this paper we discuss methods to estimate a monotone frequency of species
in a population when the ordering of species is unknown.
The question arises from [5], where the case of known order was taken
into account, and the method is inspired by [2].
We discuss first a regression approach that however only leads to the
trivial solution, and then a likelihood approach that allows some generali-
sations and provides inspiration for future work. We discuss existence and
uniqueness of the solution, and future work might be related to discussing
consistency as well as asymptotic distribution results and if possible to look
for an analytic expression of it.}},
  author       = {{Greselin, Pietro}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Maximum likelihood estimation of a monotone probability mass function with unknown labels}},
  year         = {{2019}},
}