Statistical inference for a class of multivariate negative binomial distributions

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Abstract

This paper considers statistical inference procedures for a class of models for positively correlated count variables called α-permanental random fields, and which can be viewed as a family of multivariate negative binomial distributions. Their appealing probabilistic properties have earlier been studied in the literature, while this is the first statistical paper on α-permanental randomfields. The focus is on maximum likelihood estimation, maximum quasi-likelihood estimation and on maximum composite likelihood estimation based on uni- and bivariate distributions.
Furthermore, new results for α-permanents and for a bivariate α-permanental random field are presented.
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Original languageEnglish
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages25
Publication statusPublished - Aug 2010
SeriesResearch Report Series
NumberR-2010-10
ISSN1399-2503

Keywords

  • composite likelihood
  • doubly stochastic construction
  • maximum likelihood
  • quasi-likelihood

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