Semiparametric maximum likelihood probability density estimation.

A comprehensive methodology for semiparametric probability density estimation is introduced and explored. The probability density is modelled by sequences of mostly regular or steep exponential families generated by flexible sets of basis functions, possibly including boundary terms. Parameters are...

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Autor principal:	Frank Kwasniok
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/cd5011ef240b492cb7b460bc5287edd5
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spelling	oai:doaj.org-article:cd5011ef240b492cb7b460bc5287edd52021-12-02T20:07:43ZSemiparametric maximum likelihood probability density estimation.1932-620310.1371/journal.pone.0259111https://doaj.org/article/cd5011ef240b492cb7b460bc5287edd52021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0259111https://doaj.org/toc/1932-6203A comprehensive methodology for semiparametric probability density estimation is introduced and explored. The probability density is modelled by sequences of mostly regular or steep exponential families generated by flexible sets of basis functions, possibly including boundary terms. Parameters are estimated by global maximum likelihood without any roughness penalty. A statistically orthogonal formulation of the inference problem and a numerically stable and fast convex optimization algorithm for its solution are presented. Automatic model selection over the type and number of basis functions is performed with the Bayesian information criterion. The methodology can naturally be applied to densities supported on bounded, infinite or semi-infinite domains without boundary bias. Relationships to the truncated moment problem and the moment-constrained maximum entropy principle are discussed and a new theorem on the existence of solutions is contributed. The new technique compares very favourably to kernel density estimation, the diffusion estimator, finite mixture models and local likelihood density estimation across a diverse range of simulation and observation data sets. The semiparametric estimator combines a very small mean integrated squared error with a high degree of smoothness which allows for a robust and reliable detection of the modality of the probability density in terms of the number of modes and bumps.Frank KwasniokPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 11, p e0259111 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Frank Kwasniok Semiparametric maximum likelihood probability density estimation.
description	A comprehensive methodology for semiparametric probability density estimation is introduced and explored. The probability density is modelled by sequences of mostly regular or steep exponential families generated by flexible sets of basis functions, possibly including boundary terms. Parameters are estimated by global maximum likelihood without any roughness penalty. A statistically orthogonal formulation of the inference problem and a numerically stable and fast convex optimization algorithm for its solution are presented. Automatic model selection over the type and number of basis functions is performed with the Bayesian information criterion. The methodology can naturally be applied to densities supported on bounded, infinite or semi-infinite domains without boundary bias. Relationships to the truncated moment problem and the moment-constrained maximum entropy principle are discussed and a new theorem on the existence of solutions is contributed. The new technique compares very favourably to kernel density estimation, the diffusion estimator, finite mixture models and local likelihood density estimation across a diverse range of simulation and observation data sets. The semiparametric estimator combines a very small mean integrated squared error with a high degree of smoothness which allows for a robust and reliable detection of the modality of the probability density in terms of the number of modes and bumps.
format	article
author	Frank Kwasniok
author_facet	Frank Kwasniok
author_sort	Frank Kwasniok
title	Semiparametric maximum likelihood probability density estimation.
title_short	Semiparametric maximum likelihood probability density estimation.
title_full	Semiparametric maximum likelihood probability density estimation.
title_fullStr	Semiparametric maximum likelihood probability density estimation.
title_full_unstemmed	Semiparametric maximum likelihood probability density estimation.
title_sort	semiparametric maximum likelihood probability density estimation.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/cd5011ef240b492cb7b460bc5287edd5
work_keys_str_mv	AT frankkwasniok semiparametricmaximumlikelihoodprobabilitydensityestimation
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Semiparametric maximum likelihood probability density estimation.

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