目共轭四元数矩阵积与Hadamard积的特征值的一些不等式

给出了一些四元数自共轭矩阵积与Ｈａｄａｍａｒｄ积的不等式．由此表明在很多情况下四元数自共轭矩阵积与Ｈａｄａｍａｒｄ积的性质是相似的．     

“M矩阵的Hadamard不等式”的注记

文献[1]研究了具有广泛实际背景的M矩阵的不等式。本文指出了文献[1]的主要结果,即其定理1和定理3为著名的Hadamard-Fischer不等式的特款。     

Consistent testing for non‐correlation of two cointegrated ARMA time series

A consistent approach to the problem of testing non‐correlation between two univariate infinite‐order autoregressive models was proposed by Hong (1996). His test is based on a weighted sum of squares of residual cross‐correlations, with weights depending on a kernel function. In this paper, the author follows Hong's approach to test non‐correlation of two cointegrated (or partially non‐stationary) ARMA time series. The test of Pham, Roy & Cédras (2003) may be seen as a special case of his approach, as it corresponds to the choice of a truncated uniform kernel. The proposed procedure remains valid for testing non‐correlation between two stationary invertible multivariate ARMA time series. The author derives the asymptotic distribution of his test statistics under the null hypothesis and proves that his procedures are consistent. He also studies the level and power of his proposed tests in finite samples through simulation. Finally, he presents an illustration based on real data.     

复杂体系药物分析对现代分析仪器的呼唤

复杂体系药物分析正面临在中药现代化进程中寻找各种生命现象物质基础的任务。对现代分析仪器的需求是 研制面向任务的 基于新原理、新技术以及由新理念(仪器=D/A(A/D)+CPU+software)指导的具有我国自主知识产权的世界一流水平的新型分析仪器。     

Revisiting asymmetric marriage rules

Although generalized exchange remains an emblematical model of alliance theory, characterizing matrimonial systems as pertaining to this model is tricky. The necessary condition of generalized exchange is the deliberate preference for asymmetric exchanges. Given a marriage dataset, can we determine whether the observed pattern is due to the realization of a social norm enjoining symmetric or asymmetric exchange or is the result of random processes? Here, relevant probabilities and indexes are established in the framework of graph theory, and are validated using a demographic individual-based model. The methods are applied to three datasets from the literature, allowing to assess with great confidence that the observed marriage configurations were not random.     

D-Optimal Designs for Covariate Parameters in Block Design Set Up

The problem considered is that of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non stochastic controllable covariates, when N = 2(mod 4), N being the total number of observations. It is clear that when N ≠ 0 (mod 4), it is not possible to find designs attaining minimum variance for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters were established when each of the covariates belongs to the interval [?1, 1]. Some constructions of D-optimal design have been provided for symmetric balanced incomplete block design (SBIBD) with parameters b = v, r = k = v ? 1, λ =v ? 2 when k = 2 (mod 4) and b is an odd integer.     

Supersaturated designs of projectivity P=3 or near P=3

Supersaturated designs offer a potentially useful way to investigate many factors in few experiments i.e. typical screening situations. Their design properties have mainly been evaluated based on their ability to identify and estimate main effects. Projective properties have received little attention. In this paper we show how to construct two-level supersaturated designs for 2(n−2) factors in n runs (n a multiple of four) of projectivity P=3 or near projectivity P=3 from orthogonal non-regular two-level designs. The designs obtained also have favourable properties such as low maximum absolute value of the inner product between a main effect column and a two-factor interaction column and relatively few types of different projections onto subsets consisting of three factor columns.     

Foldover Conference Designs for Screening Experiments

A conference matrix is a square matrix C with zeros on the diagonal and ±1s off the diagonal, such that C ^T C = CC ^T  = (n ? 1)I, where I is the identity matrix. Conference matrices are an important class of combinatorial designs due to their many applications in several fields of science, including statistical-experimental designs, telecommunications, elliptic geometry, and more. In this article, conference matrices and their full foldover design are combined together to obtain an alternative method for screening active factors in complicated problems. This method provides a model-independent estimate of the set of active factors and also gives a linearity test for the underlying model.     

A limit theorem on moment convergence of centered spectral statistics of random matrices

ABSTRACT

The eigenvalues of a random matrix are a sequence of specific dependent random variables, the limiting properties of which are one of interesting topics in probability theory. The aim of the article is to extend some probability limiting properties of i.i.d. random variables in the context of the complete moment convergence to the centered spectral statistics of random matrices. Some precise asymptotic results related to the complete convergence of p-order conditional moment of Wigner matrices and sample covariance matrices are obtained. The proofs mainly depend on the central limit theorem and large deviation inequalities of spectral statistics.