Asymptotic results for multinomial models

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Abstract

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.

Original languageEnglish
Article number2173
JournalSymmetry
Volume13
Issue number11
DOIs
Publication statusPublished - 12 Nov 2021

Keywords

  • Classification
  • Confidence ellipsoids
  • Covariance matrices
  • Limit distributions
  • Non-linear models

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