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On Quadratic Forms of Multivariate t Distribution with Applications |
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| Authors: | Jian-Ying Rong Zhi-Feng Lu Xu-Qing Liu |
| Institution: | 1. Department of Foundation Courses , Huai'an College of Information Technology , Huai'an , PR China jyrong98@gmail.com;3. School of Science , Nantong University , Nantong , PR China;4. Faculty of Mathematics and Physics , Huaiyin Institute of Technology , Huai'an , PR China |
| Abstract: | This note mainly aims to illustrate that some quadratic problems are robust in a sense with respect to the probabilistic distributions involved. The secondary moments of the quadratic forms of a multivariate t distribution are calculated. Then, the resulting formulae are applied to the quadratic problems of quadratic sufficiency and quadratic prediction. It is shown by revisiting the two problems that the same conclusions hold when the multivariate normal distribution is replaced with a multivariate t distribution. |
| Keywords: | Multivariate t distribution Optimal invariant quadratic unbiased predictor Optimal invariant quadratic potentially biased predictor Quadratic form Quadratic prediction Quadratic sufficiency |