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Case-deletion Influence Measures for the Data from Multivariate t Distributions

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  • Feng-Chang Xie
  • Bo-Cheng Wei
  • Jin-Guan Lin

Abstract

For the data from multivariate t distributions, it is very hard to make an influence analysis based on the probability density function since its expression is intractable. In this paper, we present a technique for influence analysis based on the mixture distribution and EM algorithm. In fact, the multivariate t distribution can be considered as a particular Gaussian mixture by introducing the weights from the Gamma distribution. We treat the weights as the missing data and develop the influence analysis for the data from multivariate t distributions based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. Several case-deletion measures are proposed for detecting influential observations from multivariate t distributions. Two numerical examples are given to illustrate our methodology.

Suggested Citation

  • Feng-Chang Xie & Bo-Cheng Wei & Jin-Guan Lin, 2007. "Case-deletion Influence Measures for the Data from Multivariate t Distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(8), pages 907-921.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:8:p:907-921
    DOI: 10.1080/02664760701590574
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    References listed on IDEAS

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    1. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
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    Cited by:

    1. Matos, Larissa A. & Lachos, Victor H. & Balakrishnan, N. & Labra, Filidor V., 2013. "Influence diagnostics in linear and nonlinear mixed-effects models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 450-464.
    2. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.
    3. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
    4. Li, Ai-Ping & Xie, Feng-Chang, 2012. "Diagnostics for a class of survival regression models with heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4204-4214.

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