随机张量的高斯分布
On Tensor Gaussian Distributions
摘要:
本文首先介绍一般多元高斯分布，包括随机向量高斯分布和随机矩阵高斯分布，研究了其基本性质，重点引进随机张量高斯分布，并研究了随机张量高斯分布的基本性质。
Abstract:
In this paper, we first introduce the multivariate Gaussian distributions, including the Gaussian distribution of a random vector and the Gaussian distribution of a random matrix. Some basic properties of those Gaussian distributions are also investigated. We then introduce the tensor Gaussian distribution of a random matrix, and present some basic properties for tensor Gaussian distribution.
参考文献
|
[1]
|
Chikuse, Y. (2008) The Matrix Angular Central Gaussian Distribution. Journal of Multivariate Analysis, 33, 265-274.
https://doi.org/10.1016/0047-259X(90)90050-R
|
|
[2]
|
尉迟江. 对高斯分布函数形式的推导[J]. 统计与信息论坛, 2009, 24(5): 3-6.
|
|
[3]
|
熊焰, 赵铁山. 金融资产收益率分布的混合高斯分布模型[J]. 统计与决策, 2004(12): 26.
|
|
[4]
|
张乃根. 经济学分析法学的理论基石——“高斯原理”评介[J]. 政治与法律, 1991(2): 54-56.
|
|
[5]
|
邓改革. 天文时间序列的分析研究[D]: [硕士学位论文]. 广州: 广州大学, 2013.
|
|
[6]
|
徐甲文, 徐松涛. 指数或高斯分布信号的MSE量化器的简捷设计[J]. 北京航空航天大学学报, 1997(3): 404-408.
|
|
[7]
|
李建泉. 正态分布高斯推证法释疑[J]. 测绘地理信息, 1991(1): 35-37.
|
|
[8]
|
王海涌, 费峥红, 王新龙. 基于高斯分布的星像点精确模拟及质心计算[J]. 光学精密工程, 2009, 17(7): 1672-1677.
|
|
[9]
|
Kollo, T. and Von Rosen, D. (2005) Advanced Multivariate Statistics with Matrices. Springer Netherlands, 81-82, 123-135.
|
|
[10]
|
Muller, K.E. and Stewart, P.W. (2006) Linear Model Theory. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 7-8.
https://doi.org/10.1002/0470052147
|
|
[11]
|
Kolda, T.G. and Badel, B.W. (2009) Tensor Decompositions and Ap-plications. Sandia Report, 51, 455-500.
https://doi.org/10.1137/07070111X
|
|
[12]
|
Qi, L. and Luo, Z. (2017) Tensor Analysis: Spectral Theory and Spectral Tensors. SIAM.
https://doi.org/10.1137/1.9781611974751
|