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Maximizing leave-one-out likelihood for the location parameter of unbounded densities

Podgorski, Krzysztof LU and Wallin, Jonas LU (2015) In Annals of the Institute of Statistical Mathematics 67(1). p.19-38
Abstract
We propose simple estimation of the location parameter for a density that is unbounded at the mode. The estimator maximizes a modified likelihood in which the singular term in the full likelihood is left out, whenever the parameter value approaches a neighborhood of the singularity location. The consistency and super-efficiency of this maximum leave-one-out likelihood estimator is shown through a direct argument. The importance for estimation within parametric families is discussed and illustrated by an example involving the gamma mixture of normal distributions.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Unbounded likelihood, Location parameter, Super-efficiency, Generalized, asymmetric Laplace distribution
in
Annals of the Institute of Statistical Mathematics
volume
67
issue
1
pages
19 - 38
publisher
Springer
external identifiers
  • wos:000347692100002
  • scopus:84921068789
ISSN
0020-3157
DOI
10.1007/s10463-013-0437-6
language
English
LU publication?
yes
id
56487e86-c52f-49d2-a20b-a917357bd6ba (old id 5075977)
date added to LUP
2015-02-25 17:02:51
date last changed
2017-01-01 05:20:17
@article{56487e86-c52f-49d2-a20b-a917357bd6ba,
  abstract     = {We propose simple estimation of the location parameter for a density that is unbounded at the mode. The estimator maximizes a modified likelihood in which the singular term in the full likelihood is left out, whenever the parameter value approaches a neighborhood of the singularity location. The consistency and super-efficiency of this maximum leave-one-out likelihood estimator is shown through a direct argument. The importance for estimation within parametric families is discussed and illustrated by an example involving the gamma mixture of normal distributions.},
  author       = {Podgorski, Krzysztof and Wallin, Jonas},
  issn         = {0020-3157},
  keyword      = {Unbounded likelihood,Location parameter,Super-efficiency,Generalized,asymmetric Laplace distribution},
  language     = {eng},
  number       = {1},
  pages        = {19--38},
  publisher    = {Springer},
  series       = {Annals of the Institute of Statistical Mathematics},
  title        = {Maximizing leave-one-out likelihood for the location parameter of unbounded densities},
  url          = {http://dx.doi.org/10.1007/s10463-013-0437-6},
  volume       = {67},
  year         = {2015},
}