Diagnostics in multivariate generalized Birnbaum-Saunders regression models

Carolina Marchant, VICTOR ELISEO LEIVA SANCHEZ, Francisco José A. Cysneiros, Juan F. Vivanco

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44 Scopus citations

Abstract

Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.

Original languageEnglish
Pages (from-to)2829-2849
Number of pages21
JournalJournal of Applied Statistics
Volume43
Issue number15
DOIs
StatePublished - 17 Nov 2016

Keywords

  • Birnbaum–Saunders distributions
  • global and local influence
  • goodness-of-fit
  • multivariate data analysis
  • R software

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