奇异增长曲线模型中回归系数阵的最优估计

讨论了协差阵可能奇异情形下回归系数阵的最优估计，作为特例给出了协差阵非奇异时回归系数阵的最优估计，同时给出了最小二乘估计与最优估计相等的条件．     

Advanced MCMC methods for sampling on diffusion pathspace

The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte-Carlo methods. We study here an advanced version of familiar Markov-chain Monte-Carlo (MCMC) algorithms that sample from target distributions defined as change of measures from Gaussian laws on general Hilbert spaces. Such a model structure arises in several contexts: we focus here at the important class of statistical models driven by diffusion paths whence the Wiener process constitutes the reference Gaussian law. Particular emphasis is given on advanced Hybrid Monte-Carlo (HMC) which makes large, derivative-driven steps in the state space (in contrast with local-move Random-walk-type algorithms) with analytical and experimental results. We illustrate its computational advantages in various diffusion processes and observation regimes; examples include stochastic volatility and latent survival models. In contrast with their standard MCMC counterparts, the advanced versions have mesh-free mixing times, as these will not deteriorate upon refinement of the approximation of the inherently infinite-dimensional diffusion paths by finite-dimensional ones used in practice when applying the algorithms on a computer.     

有丢失或附加观测值模型协方差的极大似然估计

讨论多元正态总体协方差的极大似然估计值在有丢失和附加观测值条件下的求法，同时给出了相应的极大似然估计值公式     

Redefined relativistic thermodynamics based on the Nakamura formalism

By using the concept of volume introduced by Nakamura in relativistic thermodynamics, a relativistic thermodynamical theory is proposed. A comparison is presented between the new theory, the van Kampen covariant theory and the Rohrlich proposal. A relativistic thermometer is proposed by using the Unruh-DeWitt detector.     

协方差矩阵的乘积及其迹的估计

对于两个不同总体的协方差矩阵$\Sigma_1$和$\Sigma_2$,估计其乘积$\Sigma_1 \Sigma_2$及乘积的迹$\trace(\Sigma_1 \Sigma_2)$是统计推断问题的关键步骤. 首先,构造$\Sigma_1 \Sigma_2$的几个等价估计,同时对于任意的正整数$m,n$建立了$\Sigma_1^m \Sigma_2^n$ 和 $(\Sigma_1 \Sigma_2)^m$的无偏估计。其次,利用$\Sigma_1 \Sigma_2$ 的等价估计,发现了$\trace(\Sigma_1 \Sigma_2)$的多个常用估计量是相等的. 最后,基于上述发现,证明了两个常用的检验统计量(被用于检验两个协方差矩阵是否相等)是渐近等价的.     

Wiener过程分布密度的矩阵算法

在随机过程的理论及其应用中．Ｗｉｅｎｅｒ过程起着基本的作用．本文结出用矩阵的初等变换，建立Ｗｉｅｎｅｒ过程ｐ．ｄ，ｆ的一个崭新的方法；此方法，对理解过程的统计特性，掌握过程的ｐ，ｄ，ｆ的结构等，均是有益的．     

Covariance NMR spectroscopy by singular value decomposition

Covariance NMR is demonstrated for homonuclear 2D NMR data collected using the hypercomplex and TPPI methods. Absorption mode 2D spectra are obtained by application of the square-root operation to the covariance matrices. The resulting spectra closely resemble the 2D Fourier transformation spectra, except that they are fully symmetric with the spectral resolution along both dimensions determined by the favorable resolution achievable along omega2. An efficient method is introduced for the calculation of the square root of the covariance spectrum by applying a singular value decomposition (SVD) directly to the mixed time-frequency domain data matrix. Applications are shown for 2D NOESY and 2QF-COSY data sets and computational benchmarks are given for data matrix dimensions typically encountered in practice. The SVD implementation makes covariance NMR amenable to routine applications.     

On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations

The asymptotic distribution of some test criteria for a covariance matrix are derived under local alternatives. Except for the existence of some higher moments, no assumption as to the form of the distribution function is made. As an illustration, a case of t distribution included normal model is considered and the power of the likelihood ratio test and Nagao's test for sphericity, as described in Srivastava and Khatri and Anderson, is computed. Also, the power is computed using the bootstrap method. In the case of t distribution, the bootstrap approximation does not appear to be as good as the one obtained by the asymptotic expansion method.     

Behavior of Stochastic Shear Beams Under Random Loading via Stochastic Variational Principles

In this study we derive, apparently for the first time in the literature, some exact solutions for the shear beams with stochastic flexibility, when these beams are acted upon by the random loading. The importance of these solutions lies in the fact that they can serve as benchmark solutions, to which the approximate solutions of various nature can be compared. Then we formulate stochastic variational principles, the first principle governs the behavior of the mean displacement, whereas the second principle is satisfied by the displacements covariance function. These variational principles allow us to formulate approximate techniques for the cases in which the exact solution is presently unavailable. In particular, we develop a stochastic version of the Rayleigh–Ritz method. Several examples are evaluated to shed more light on the probabilistic behavior of randomly excited structures possessing random flexibility.