Distribution of the likelihood ratio criterion for testing Σ = Σ0, μ = μ0

The exact null distribution of the likelihood ratio criterion for testing H₀: Σ = Σ₀ and μ = μ₀ against alternatives H₁: Σ ≠ Σ₀ or μ ≠ μ₀ in N_p(μ, Σ) has been obtained as (a) a chi-square series and (b) a beta series. Percentage points have been tabulated for p = 2(1) 6, α = .005, .01, .025, .05, .1, and .25 and various values of sample size N.     

Analysis and elimination of artifacts in indirect covariance NMR spectra via unsymmetrical processing

Indirect covariance NMR offers an alternative method of extracting spin-spin connectivity information via the conversion of an indirect-detection heteronuclear shift-correlation data matrix to a homonuclear data matrix. Using an IDR (inverted direct response)-HSQC-TOCSY spectrum as a starting point for the indirect covariance processing, a spectrum that can be described as a carbon-carbon COSY experiment is obtained. These data are analogous to the autocorrelated 13C-13C double quantum INADEQUATE experiment except that the indirect covariance NMR spectrum establishes carbon-carbon connectivities only between contiguous protonated carbons. Cyclopentafuranone and the complex polynuclear heteroaromatic naphtho[2',1':5,6]-naphtho[2',1':4,5]thieno[2,3-c]quinoline are used as model compounds. The former is a straightforward example because of its well-resolved proton spectrum, while the latter, which has considerable resonance overlap in its congested proton spectrum, gives rise to two types of artifact responses that must be considered when using the indirect covariance NMR method.     

On Mad and Comedians

A popular robust measure of dispersion of a random variable (rv) X is the median absolute deviation from the median med(|X - med(X)|), MAD for short, which is based on the median med(X) of X. By choosing Y = X, the MAD turns out to be a special case of the comedian med((X - med(X))(Y - med(Y))), which is a robust measure of covariance between rvs X and Y. We investigate the comedian in detail, in particular in the normal case, and establish strong consistency and asymptotic normality of empirical counterparts. This leads to a robust competitor of the coefficient of correlation as an asymptotic level--statistic for testing independence of X and Y. An example shows the weird fact that knowledge of the population med(X) does not necessarily pay (in the sense of asymptotic relative efficiency) when estimating the MAD.     

Multiple outlier detection in multivariate data using self-organizing maps title

Summary  The problem of detection of multidimensional outliers is a fundamental and important problem in applied statistics. The unreliability of multivariate outlier detection techniques such as Mahalanobis distance and hat matrix leverage has led to development of techniques which have been known in the statistical community for well over a decade. The literature on this subject is vast and growing. In this paper, we propose to use the artificial intelligence technique ofself-organizing map (SOM) for detecting multiple outliers in multidimensional datasets. SOM, which produces a topology-preserving mapping of the multidimensional data cloud onto lower dimensional visualizable plane, provides an easy way of detection of multidimensional outliers in the data, at respective levels of leverage. The proposed SOM based method for outlier detection not only identifies the multidimensional outliers, it actually provides information about the entire outlier neighbourhood. Being an artificial intelligence technique, SOM based outlier detection technique is non-parametric and can be used to detect outliers from very large multidimensional datasets. The method is applied to detect outliers from varied types of simulated multivariate datasets, a benchmark dataset and also to real life cheque processing dataset. The results show that SOM can effectively be used as a useful technique for multidimensional outlier detection.     

Semiparametric spatio-temporal covariance models with the ARMA temporal margin

Starting from a purely spatial variogram, this paper derives a class of semiparametric spatio-temporal covariance models that are stationary in time but not necessarily stationary in space. In particular, we obtain spatio-temporal covariance models with the continuous-time autoregressive and moving average (ARMA) temporal margin and long-range dependent spatial margin.     

Panel模型中常见估计的比较

本文研究了Panel模型中回归系数常见估计的比较问题,给出了在Pitman准则,协方差阵准则和广义均方误差准则下最小二乘估计,Within估计,Between估计及两步估计之间的优良性比较结果.特别地,本文证明了在Pitman准则下最小二乘估计一致地优于Between估计.     

Role of Covariance Correlation Tensor in Establishment of Criterion of Quantum Entanglement

This article discusses the role of covariance correlation tensor in the establishment of the criterion of quantum entanglement. It gives a simple example to show the powerfulness in the treatment of quantum dense coding, and illustrates the fact that this method also provides theoretical basis for establishing corresponding knotted pictures.     

A Moment Specification Algorithm for Control of Nonlinear Systems Driven by Gaussian White Noise

Covariance control methods have been applied to linearstochastic multivariable control systems to ensure good behavior of eachstate variable separately. Recent attempts to extend these ideas tononlinear systems have been reported, including an example of a systemexhibiting hysteresis nonlinearity which employed describing functions.As nonlinearities, including hysteresis, occur frequently in structuralsystems, the development of effective control algorithms to accommodatethem is desirable. Recently, the authors designed covariance controllersfor several hysteretic systems using the method of stochastic equivalentlinearization. Performance of the closed loop system employing thecovariance control was verified through simulation. In the present work,a new control design method is adopted that uses the principle ofmaximum entropy, which has been used as an alternative procedure forclosure of moment equations arising in stochastic dynamical systems. Themaximum entropy-based method leads to a result equivalent to that ofstochastic linearization when covariances alone are specified; however,the method readily accommodates the specification of higher orderresponse moments.     

Consistent estimation of covariation under nonsynchronicity

We present a methodology to estimate the covariance of two time series when they are sampled from continuous semimartingales at general stopping times in a nonsynchronous manner. Approximation error bounds being explored, the estimators are shown to be consistent as the size of the sampling intervals tends to zero. The methodology is easy to be implemented with potentially broad applications, especially in financial modeling and analysis involving high-frequency transaction data. The results generalize those recently obtained by obtained by Hayashi and Yoshida (2005, Bernoulli 11(2):359–379)      

非线性模型中方差和协方差分量的Bayes估计

本文采用Bayes方法从有逆gamma先验信息出发,得到了非张性模型中方差和协方差分量的估计,本文中的方差和协方差分量包含相关系数,而其他学者提出的线性模型中方差和协方差分量的Bayes估计只是本文的特殊情况.