Linear estimating equations for exponential families with application to Gaussian linear concentration models

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Linear estimating equations for exponential families with application to Gaussian linear concentration models. / Forbes, Peter G.M. ; Lauritzen, Steffen L.

I: Linear Algebra and Its Applications, Bind 473, 2015, s. 261-283 .

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Forbes, PGM & Lauritzen, SL 2015, 'Linear estimating equations for exponential families with application to Gaussian linear concentration models', Linear Algebra and Its Applications, bind 473, s. 261-283 . https://doi.org/10.1016/j.laa.2014.08.015

APA

Forbes, P. G. M., & Lauritzen, S. L. (2015). Linear estimating equations for exponential families with application to Gaussian linear concentration models. Linear Algebra and Its Applications, 473, 261-283 . https://doi.org/10.1016/j.laa.2014.08.015

Vancouver

Forbes PGM, Lauritzen SL. Linear estimating equations for exponential families with application to Gaussian linear concentration models. Linear Algebra and Its Applications. 2015;473:261-283 . https://doi.org/10.1016/j.laa.2014.08.015

Author

Forbes, Peter G.M. ; Lauritzen, Steffen L. / Linear estimating equations for exponential families with application to Gaussian linear concentration models. I: Linear Algebra and Its Applications. 2015 ; Bind 473. s. 261-283 .

Bibtex

@article{30bc93c0e558476f8fe13e729e39abf8,
title = "Linear estimating equations for exponential families with application to Gaussian linear concentration models",
abstract = "In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator Hyv{\"a}rinen (1905) provides an alternative where this normalization constant is not required. For an exponential family, e.g. a Gaussian linear concentration model, the corresponding estimating equations become linear (Almeida and Gidas 1993) and the score matching estimator is shown to be consistent and asymptotically normally distributed as the number of observations increase to infinity, although not necessarily efficient. For linear concentration models that are also linear in the covariance (Jensen 1988) we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries (H{\o}jsgaard and Lauritzen 2008) form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case.",
author = "Forbes, {Peter G.M.} and Lauritzen, {Steffen L.}",
year = "2015",
doi = "10.1016/j.laa.2014.08.015",
language = "English",
volume = "473",
pages = "261--283 ",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Linear estimating equations for exponential families with application to Gaussian linear concentration models

AU - Forbes, Peter G.M.

AU - Lauritzen, Steffen L.

PY - 2015

Y1 - 2015

N2 - In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator Hyvärinen (1905) provides an alternative where this normalization constant is not required. For an exponential family, e.g. a Gaussian linear concentration model, the corresponding estimating equations become linear (Almeida and Gidas 1993) and the score matching estimator is shown to be consistent and asymptotically normally distributed as the number of observations increase to infinity, although not necessarily efficient. For linear concentration models that are also linear in the covariance (Jensen 1988) we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries (Højsgaard and Lauritzen 2008) form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case.

AB - In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator Hyvärinen (1905) provides an alternative where this normalization constant is not required. For an exponential family, e.g. a Gaussian linear concentration model, the corresponding estimating equations become linear (Almeida and Gidas 1993) and the score matching estimator is shown to be consistent and asymptotically normally distributed as the number of observations increase to infinity, although not necessarily efficient. For linear concentration models that are also linear in the covariance (Jensen 1988) we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries (Højsgaard and Lauritzen 2008) form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case.

U2 - 10.1016/j.laa.2014.08.015

DO - 10.1016/j.laa.2014.08.015

M3 - Journal article

VL - 473

SP - 261

EP - 283

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 128111395