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Fisher信息阵在矩阵不等式证明中的应用 被引量：1

Applications of Fisher Information Matrix in the Proof of Matrix Inequalities
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摘要 利用多元正态分布以及Fisher信息阵的单调性和可加性,证明了几个常见的矩阵不等式和多参数Cramer-Rao不等式,而证明的过程没有使用矩阵理论。 We use multivariate normal distributions and basic properties of Fisher information matrix such as monotonicity, additivity to prove several common matrix inequalities and multi--parameter Cramer--Rao inequality. No matrix theory is used in the process of proof.
作者 黄翔 石贤汇
机构地区 合肥工业大学数学学院 池州学院数学与计算科学系
出处 《安庆师范学院学报（自然科学版）》 2010年第1期5-6,共2页 Journal of Anqing Teachers College(Natural Science Edition)
关键词 矩阵不等式 FISHER信息阵 线性模型 多元正态分布 matrix inequality, Fisher information matrix, linear model, multivariate normal distribution
分类号 O212.1 [理学—概率论与数理统计]
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参考文献5

  • 1Abram Kagan,C. Radhakrishna Rao. Some properties and applications of the efficient Fisher score[J].Journal of Statistical Planning and Inference, 2003 (116) : 343- 352.
  • 2C. vigant and J. -F. bercher. On Fisher information inequalities and score function in non-invertible linear systems[J]. Journal of inequalities in pure and applied mathematics,Article, 2003,4(4):1-9.
  • 3C. Radhakrishna Rao. Statistical proofs of some matrix inequalities[J]. Linear Algebra and its Applications, 2000 (321) :307-320.
  • 4王松桂.矩阵不等式[M].北京:科学出版社.2006:33-36.
  • 5Abram Kagan. Another look at the Cramer-Rao inequality[J]. The American statistician, 2001,55 (3) : 211- 212.

共引文献52

同被引文献9

  • 1Zimmerman, D. L. , Nunez- Anton, V. Parametric modelling of growth curve data: an overview (with discussion) [ J]. Test , 2001, 10 (1) :1 - 73.
  • 2Bosq, D. Linear Processes in Function Spaces[ J ]. Lecture Note in Statistics, 2000,6:149.
  • 3Abraham, C., Biau, G., Cadre, B. Simple estimation of the mode of a multivariate density[J]. Canad. J. Statist. ,2003a ,31:23 - 34.
  • 4Eva Herrmann, Klaus Ziegler. Rate of consistency for nonparametric estimation of the mode in absence of smoothness assumptions [ J ]. Stochastic Process. Appl. ,2004,68:359-368.
  • 5Ferraty, F., Vieu, P. Nonparametric Functional Data Analysis: Theory and Practice[ M]. Springer Series in Statistics, Springer, NewYork. 2006.
  • 6Perdond, G. C, &Louzada - Neto, F. Interval estimation for the paranleters of the modified Weibull distribution model with censored data: A simulation study[ J]. Tendencias em Matemetiea Aplicada e Computational, 2008,9:437 -446.
  • 7Kim, Y- M. , & Jhun, M. Cure rate model with interval censored data[J]. Statistics in Medecine,2008,27:3 -14.
  • 8Dabo -Nianga, S, Ferraty, F. , Vieu, P. On the using of modal curves for radar wavefonns classification [ J ]. Far East J. Theoret. Statist. 2006b,11:102 - 108.
  • 9Cadre, B. Contributions "a 1' 'etude de certains phenomenes stochastiques [ M ] ( in french). Habilitation "a Diriger des Recherches, Universit'e Montpellierl1,2002.

引证文献1

安庆师范学院学报（自然科学版）
2010年 第1期

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