TY - JOUR
T1 - Some results on the truncated multivariate t distribution
AU - Ho, Hsiu J.
AU - Lin, Tsung I.
AU - Chen, Hsuan Yu
AU - Wang, Wan Lun
N1 - Funding Information:
The authors would like to express their deepest gratitude to the Chief Editor, the Associate Editor and one anonymous referee for carefully reading the paper and for their great help in improving the paper. This research was supported by the National Science Council of Taiwan (Grant nos. NSC99-2118-M-005-001-MY2 and NSC99-2118-M-035-004 ).
PY - 2012/1
Y1 - 2012/1
N2 - The use of truncated distributions arises often in a wide variety of scientific problems. In the literature, there are a lot of sampling schemes and proposals developed for various specific truncated distributions. So far, however, the study of the truncated multivariate t (TMVT) distribution is rarely discussed. In this paper, we first present general formulae for computing the first two moments of the TMVT distribution under the double truncation. We formulate the results as analytic matrix expressions, which can be directly computed in existing software. Results for the left and right truncation can be viewed as special cases. We then apply the slice sampling algorithm to generate random variates from the TMVT distribution by introducing auxiliary variables. This strategic approach can result in a series of full conditional densities that are of uniform distributions. Finally, several examples and practical applications are given to illustrate the effectiveness and importance of the proposed results.
AB - The use of truncated distributions arises often in a wide variety of scientific problems. In the literature, there are a lot of sampling schemes and proposals developed for various specific truncated distributions. So far, however, the study of the truncated multivariate t (TMVT) distribution is rarely discussed. In this paper, we first present general formulae for computing the first two moments of the TMVT distribution under the double truncation. We formulate the results as analytic matrix expressions, which can be directly computed in existing software. Results for the left and right truncation can be viewed as special cases. We then apply the slice sampling algorithm to generate random variates from the TMVT distribution by introducing auxiliary variables. This strategic approach can result in a series of full conditional densities that are of uniform distributions. Finally, several examples and practical applications are given to illustrate the effectiveness and importance of the proposed results.
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U2 - 10.1016/j.jspi.2011.06.006
DO - 10.1016/j.jspi.2011.06.006
M3 - Article
AN - SCOPUS:80052298393
SN - 0378-3758
VL - 142
SP - 25
EP - 40
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1
ER -