Convergence Theorems in Multinomial Saturated and Logistic Models

Q3 Mathematics Revista Colombiana De Estadistica Pub Date : 2020-07-01 DOI:10.15446/rce.v43n2.79151

E. Orozco-Acosta, Humberto Llinás-Solano, Javier Fonseca-Rodríguez

引用次数: 0

Abstract

In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demonstrated. Furthermore, properties are identified and, based on an asymptotic theory, convergence theorems are tested for score vectors and information matrices of both models. Finally, an application of this theory is presented and assessed using data from the R statistical program.

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多项饱和和Logistic模型的收敛定理

本文对响应变量取R≥2个水平时的logistic和饱和多项模型进行了理论研究。给出并证明了两个模型参数的最大似然估计的存在性和计算的几个定理。此外，在渐近理论的基础上，对两种模型的分数向量和信息矩阵的收敛定理进行了检验。最后，介绍了该理论的一个应用，并使用R统计程序中的数据进行了评估。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Revista Colombiana De Estadistica STATISTICS & PROBABILITY-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Colombian Journal of Statistics publishes original articles of theoretical, methodological and educational kind in any branch of Statistics. Purely theoretical papers should include illustration of the techniques presented with real data or at least simulation experiments in order to verify the usefulness of the contents presented. Informative articles of high quality methodologies or statistical techniques applied in different fields of knowledge are also considered. Only articles in English language are considered for publication. The Editorial Committee assumes that the works submitted for evaluation have not been previously published and are not being given simultaneously for publication elsewhere, and will not be without prior consent of the Committee, unless, as a result of the assessment, decides not publish in the journal. It is further assumed that when the authors deliver a document for publication in the Colombian Journal of Statistics, they know the above conditions and agree with them.