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41.
本文构造出正态线性模型误差协差阵的逆矩阵的二次型的经验Bayes(ER)估计,在一定条件下证明了这种EB估计的收敛速度可任意接近于1.最后,给出了一个实例. 相似文献
42.
This is the first of a couple of papers in which the peculiar capabilities of the Hamiltonian approach to general relativity
are exploited to get both new results concerning specific technical issues, and new insights about old foundational problems of the theory. The first paper includes: (1) a critical analysis of the various concepts of symmetry
related to the Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian viewpoint, on the other. This
analysis leads, in particular, to a re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose the (not widely known)) connection
of a subgroup of them to Hamiltonian gauge transformations on-shell; (2) a re-visitation of the canonical reduction of the ADM formulation of general relativity, with particular emphasis on
the geometro-dynamical effects of the gauge-fixing procedure, which amounts to the definition of a global non-inertial, space-time laboratory. This analysis discloses the peculiar dynamical nature that the traditional definition of distant simultaneity and clock-synchronization assume in general relativity, as well as
the gauge relatedness of the “conventions” which generalize the classical Einstein's convention. (3) a clarification of the physical role of Dirac
and gauge variables, as their being related to tidal-like and generalized inertial effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle,
the Hamiltonian formalism allows to define a generalized notion of “force” in general relativity in a natural way. 相似文献
43.
A Berry--Esseen type estimate is established for a weakly associated vector random field when sums are taken over regularly growing sets. 相似文献
44.
刘金山 《纯粹数学与应用数学》1997,13(1):30-37
考虑相依回归方程系统yi=Xiβi+εi(i=1,2),E(εi)=0,Cov(εi,εj)=σijIn。记βi为βi的协方差改进估计^[1]。σij未知时,记βi为用非限定估计σij代替βi中的σij得到的两步估计,并记βi为用限定估计σij代替βi中的σij得到的两步估计,这两种两步估计的协方差中含有未知参数σij代替βi中的σij得到的两步估计,这两种两步估计的协方差中含有未知参数σij。本 相似文献
45.
Paul W. Ayers 《Journal of Chemical Sciences》2005,117(5):441-454
The electron localization measure proposed by Becke and Edgecombe is shown to be related to the covariance of the electron
pair distribution. Just as with the electron localization function, the local covariance does not seem to be, in and of itself,
a useful quantity for elucidating shell structure. A function of the local covariance, however, is useful for this purpose.
A different function, based on the hyperbolic tangent, is proposed to elucidate the shell structure encapsulated by the local
covariance; this function also seems to work better for the electron localization measure of Becke and Edgecombe. In addition,
we propose a different measure for the electron localization that incorporates both the electron localization measure of Becke
and Edgecombe and the Laplacian of the electron density; preliminary indications are that this measure is especially good
at elucidating the shell structure in valence regions. Methods for evaluating electron localization functions directly from
the electron density, without recourse to the Kohn-Sham orbitals, are discussed. 相似文献
46.
Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures have been developed to analyze such data while taking into account the resulting dependence of observations. Most of these developments require a multivariate normality distribution assumption. It is important to know whether normal theory-based inference can still be valid when applied to nonnormal hierarchical data sets. Using an analytical approach for balanced data and numerical illustrations for unbalanced data, this paper shows that the likelihood ratio statistic based on the normality assumption is asymptotically robust for many nonnormal distributions. The result extends the scope of asymptotic robustness theory that has been established in different contexts. 相似文献
47.
We consider a hypoelliptic two-parameter diffusion. We first prove a sharp upper bound in small time (s, t)[0, 1]2 for the Lp-moments of the inverse of the Malliavin matrix of the diffusion process. Second, we establish the behaviour of22 log ps, t(x, y), as ↓0, where x is the initial condition of the diffusion, =
, and ps, t(x, y) is the density of the hypoelliptic two-parameter diffusion. 相似文献
48.
Let {vij; i, J = 1, 2, …} be a family of i.i.d. random variables with E(v114) = ∞. For positive integers p, n with p = p(n) and p/n → y > 0 as n → ∞, let Mn = (1/n) Vn VnT , where Vn = (vij)1 ≤ i ≤ p, 1 ≤ j ≤ n, and let λmax(n) denote the largest eigenvalue of Mn. It is shown that
a.s. This result verifies the boundedness of E(v114) to be the weakest condition known to assure the almost sure convergence of λmax(n) for a class of sample covariance matrices. 相似文献
49.
Wulf Rehder 《Annals of the Institute of Statistical Mathematics》1980,32(1):179-185
Summary Linear unbiased estimation of the mean of a random variable in Hilbert space is treated in the typical case where the mean
belongs to a known subspace.
The best linear estimate depends on the underlying covariance operatorB
0 of the random variable. This operatorB
0, however, is rarely completely known, so that an auxiliary operatorB is used to compute a “pseudo-best” estimate. It is shown that the best and the pseudo-best estimates coincide, if and only
ifB
0
B
−1 leavesM invariant. Applications to linear regression are to be found in the references. 相似文献
50.
Bayes and empirical Bayes iteration estimators in two seemingly unrelated regression equations 总被引:3,自引:0,他引:3
WANG Lichun Institute of Applied Mathematics Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(9):1153-1168
For a system of two seemingly unrelated regression equations given by (?)(y_1 is an m×1 vector and y_2 is an n×1 vector,m≠n),employ- ing the covariance adjusted technique,we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients.We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well.Based on the mean square error (MSE) criterion,we elaborate the su- periority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown.The results obtained in this paper further show the power of the covariance adiusted approach. 相似文献