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61.
62.
The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion. 相似文献
63.
64.
A general structure of a linguistic classifier wherein sub-subclassifiers are the building blocks is suggested. Some properties of these sub-subclassifiers are proposed and proved. The physical significances of these properties are explored and it is shown that a condensed measure of belongingness of patterns to any class can be obtained which can conveniently be used for forming classification rules. 相似文献
65.
Direct approach to quantum extensions of Fisher information 总被引:1,自引:0,他引:1
By manipulating classical Fisher information and employing various derivatives of density operators, and using entirely intuitive
and direct methods, we introduce two families of quantum extensions of Fisher information that include those defined via the
symmetric logarithmic derivative, via the right logarithmic derivative, via the Bogoliubov-Kubo-Mori derivative, as well as
via the derivative in terms of commutators, as special cases. Some fundamental properties of these quantum extensions of Fisher
information are investigated, a multi-parameter quantum Cramér-Rao inequality is established, and applications to characterizing
quantum uncertainty are illustrated.
相似文献
66.
Questions of asymptotic inference are discussed for a point process model in which the conditional intensity function increases monotonically between events and drops by determined (nonrandom) amounts after each event. Parameter estimates are shown to be consistent and, except under the null hypothesis of a Poisson process, normally distributed. Under the null hypothesis, however, the Hessian matrix is not asymptotically constant, and the limiting distribution of the likelihood ratio statistics is not χ2, but has a form related to that of the Cramer-von Mises ω2 statistic for the test of goodness of fit. 相似文献
67.
K. Zografos K. Ferentinos T. Papaioannou 《Annals of the Institute of Statistical Mathematics》1989,41(3):451-460
In this paper we investigate the limiting behaviour of the measures of information due to Csiszár, Rényi and Fisher. Conditions for convergence of measures of information and for convergence of Radon-Nikodym derivatives are obtained. Our results extend the results of Kullback (1959,Information Theory and Statistics, Wiley, New York) and Kirmani (1971,Ann. Inst. Statist. Math.,23, 157–162). 相似文献
68.
Bin Meng Maozheng Guo Xiaohong Cao 《Proceedings of the American Mathematical Society》2005,133(10):3087-3096
We introduce the operator-valued free Fisher information for a random variable in an operator-valued noncommutative probability space and point out its relations to the amalgamated freeness. Using M. Frank and D. Larson's modular frame notion we can construct the conjugate variable for an operator-valued semicircle variable with conditional expectation covariance. Then we obtain its free Fisher information and show it is equal to the index of the conditional expectation. At last the conjugate variable with respect to a modular frame operator for a semicircle variable is also constructed.
69.
提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统. 相似文献
70.
We show how macroeconomic dynamics can be derived from asymmetric information. As an illustration of the utility of this approach we derive the equilibrium density, non-equilibrium densities and the equation of motion for the response to a demand shock for productivity in a simple economy. Novel consequences of this approach include a natural incorporation of time dependence into macroeconomics and a common information-theoretic basis for economics and other fields seeking to link micro-dynamics and macro-observables. 相似文献