PROOF OF A CONJECTURE OF EATON,M.L. ON THE CHARACTERISTIC FUNCTION OF THE WISHART DISTRIBUTION

• 成果类型: Article
• 署名作者: PEDDADA, SD; RICHARDS, DSP
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990455
• 发表日期: 1991
• 页码: 868-874
• 关键词: zonal-polynomials

摘要

Let m (greater-than-or-equal-to 2) be a positive integer; I(m) be the m x m identity matrix; and SIGMA and A be symmetric m x m matrices, where SIGMA is positive definite. By proving that the function phi-alpha-(A) = \I(m) - 2iA-SIGMA\-alpha is a characteristic function only if alpha element-of {0, 1/2, 1, 3/2, ..., (m - 2)/2} union [(m - 1)/2, infinity), we establish a conjecture of Eaton. A similar result is established for the rank 1 noncentral Wishart distribution and is conjectured to also be valid for any greater rank.