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

Xie, Feng-Chang, Wei, Bo-Cheng and Lin, Jin-Guan

Journal of Applied Statistics, 2007, vol. 34, issue 8, pages 907-921

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.

Keywords: Multivariate t distribution; influence analysis; EM algorithm; case-deletion; generalized Cook distance (search for similar items in EconPapers)

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