Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models

There is a difficulty in finding an estimate of the standard error (SE) of the profile likelihood estimator in the joint model of longitudinal and survival data. The difficulty is on the differentiation of an implicit function that appear in the profile likelihood estimation. We solve the difficulty...

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Detalles Bibliográficos
Autores principales: Hirose, Yuichi, Liu, Ivy
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516731/
https://www.ncbi.nlm.nih.gov/pubmed/33286050
http://dx.doi.org/10.3390/e22030278
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author Hirose, Yuichi
Liu, Ivy
author_facet Hirose, Yuichi
Liu, Ivy
author_sort Hirose, Yuichi
collection PubMed
description There is a difficulty in finding an estimate of the standard error (SE) of the profile likelihood estimator in the joint model of longitudinal and survival data. The difficulty is on the differentiation of an implicit function that appear in the profile likelihood estimation. We solve the difficulty by introducing the “statistical generalized derivative”. The derivative is used to show the asymptotic normality of the estimator with the SE expressed in terms of the profile likelihood score function.
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spelling pubmed-75167312020-11-09 Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models Hirose, Yuichi Liu, Ivy Entropy (Basel) Article There is a difficulty in finding an estimate of the standard error (SE) of the profile likelihood estimator in the joint model of longitudinal and survival data. The difficulty is on the differentiation of an implicit function that appear in the profile likelihood estimation. We solve the difficulty by introducing the “statistical generalized derivative”. The derivative is used to show the asymptotic normality of the estimator with the SE expressed in terms of the profile likelihood score function. MDPI 2020-02-28 /pmc/articles/PMC7516731/ /pubmed/33286050 http://dx.doi.org/10.3390/e22030278 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Hirose, Yuichi
Liu, Ivy
Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models
title Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models
title_full Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models
title_fullStr Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models
title_full_unstemmed Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models
title_short Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models
title_sort statistical generalized derivative applied to the profile likelihood estimation in a mixture of semiparametric models
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516731/
https://www.ncbi.nlm.nih.gov/pubmed/33286050
http://dx.doi.org/10.3390/e22030278
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AT liuivy statisticalgeneralizedderivativeappliedtotheprofilelikelihoodestimationinamixtureofsemiparametricmodels

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