Central limit theoremHermite ensemblesLaguerre ensemblesDyson Brownian motionCovariance matrixEigenvaluesBessel processes $(X_{t,k})_{t\\ge0}$ in $N$ dimensions are classified via associated root systems and multiplicity constants $k\\ge0$. They describe interacting Calogero-Moser-Suther\\-land ...
To state the results, for a positive integerdwe define a class of test functions, as follows. We sayiffhis three times partially differentiable with third partial derivatives being Lipschitz and bounded. Moreover we denote bythe class of convex sets in. Theorem 1.1 Letbe an appropriately scaled...
V. Sazonov, “Central limit theorem for random elements assuming values in Hilbert space,” Teor. Veroyat. i Prim.,9, No. 1, 43–52 (1964). Google Scholar V. M. Kruglov, “Convergence of distributions of sums of independent random variables with values in Hilbert space,” Teor. Vero...
Martingale theory is used to obtain a central limit theorem for degenerate U-statistics with variable kernels, which is applied to derive central limit theorems for the integrated square error of multivariate nonparametric density estimators. Previous approaches to this problem have employed Komlós-Major...
In consequence of these inequalities, the multivariate central limit theorem arises in the sense of the total variation. 关键词: Multivariate variational inequalities central limit theorem DOI: 10.1006/jmva.1996.0047 被引量: 10 年份: 1996 ...
高斯分布的另一种情况是当考虑多个随机变量的和时。由中心极限定理(central limit theorem (due to Laplace))知,在一定的温和条件下(certain mild conditions),一组随机变量的和,当然它本身就是一个随机变量,它的分布随着项数的增加而逐渐趋于高斯分布(Walker, 1969)。
the second factor can be applied to the multivariate central limit theorem because it is divided by \(\sqrt{n}\) . from lemma 1 and eq. ( 8 ), we obtain $$\begin{aligned} \frac{1}{\sqrt{n}}\varvec{g}(\varvec{y}_1,\ldots ,\varvec{y}_n ;\varvec{\eta }_0)\overset{...
The convergence of 1 S tof (Y , (s), ) g ( (s) | Y , ) L( ; Y ) can be justified by the central limit theorem, though it requires the variance of f (Y , (s), ) g ( (s) | Y , ) to be finite. Koopman and Shephard (2004) proposed a test to check the validity ...
Reliablevariables and drawing dependent variables from a multivariatenormal distribution; If all variables meet the univariate normality requirement then its likely that the variables meet this assumption (for larger samples, thecentral limit theoremsuggests normality). ...
2) multiple central limit theorem 多元极限定理 3) central limit theorem 中心极限定理 1. Law of Great Numbers and Central Limit Theorem of Series of Correlated Random Variables; 相关随机序列的大数定律和中心极限定理 2. Note on the almost surecentral limit theoremfor ρ~--mixing sequences.; ...