ARMA MODELS REALIZATION AND IMPULSE RESPONSES

A parallel is made between the role played by covariances in the determination of auto-regressive models and the role played by impulse responses in the determination of ARMA models.

Auto-regressive models are known to maximize the Burg-entropy under covariance constraints. Auto-regressive-moving-average models give the maximum of the Burg-entropy among processes sharing the same covariances and impulse responses up to a certain lag. Such models are constructed by iterative or algebraic methods under the different constraints.

A new recursive method of identification of the order of an ARMA model is also developed, based on the generalized reflection coefficients.     

一元n次多项式根的圆环覆盖定理

本文的主要结果是利用相容矩阵范数的性质给出了一元ｎ次多项式根的圆环覆盖定理,即一元ｎ次多项式的所有非零复根必全都落在复平面上同一个圆环区域内．特别,ｎ次二项式的所有非零复根必都落在同一个圆周上．这一结果,可以改进盖尔斯果林（Ｇｅｒｓｓｇｏｒｉｎ）的圆盘覆盖定理的结果．     

A monte carlo analysis of two spectral tests of the martingale hypothesis

Summary The size, power, and robustness properties of the Kolmogorov-Smirnov and Cramér-von Mises spectral tests of the martingale (difference) hypothesis are investigated by Monte Carlo methods. The results highlight a marked superiority of the Cramér-von Mises with respect to the Kolmogorov-Smirnov test. The paper also shows that the Cramér-von Mises test is simple to compute, more general and more powerful than other converntionally used tests.     

Robustness of the Affine Equivariant Scatter Estimator Based on the Spatial Rank Covariance Matrix

Visuri et al. (2000 Visuri, S., Koivunen, V., Oja, H. (2000). Sign and rank covariance matrices. J. Stat. Plann. Inference 91:557–575.[Crossref], [Web of Science ®] , [Google Scholar]) proposed a technique for robust covariance matrix estimation based on different notions of multivariate sign and rank. Among them, the spatial rank based covariance matrix estimator that utilizes a robust scale estimator is especially appealing due to its high robustness, computational ease, and good efficiency. Also, it is orthogonally equivariant under any distribution and affinely equivariant under elliptically symmetric distributions. In this paper, we study robustness properties of the estimator with respective to two measures: breakdown point and influence function. More specifically, the upper bound of the finite sample breakdown point can be achieved by a proper choice of univariate robust scale estimator. The influence functions for eigenvalues and eigenvectors of the estimator are derived. They are found to be bounded under some assumptions. Moreover, finite sample efficiency comparisons to popular robust MCD, M, and S estimators are reported.     

On the Spectral Decomposition in Normal Discriminant Analysis

This article enlarges the covariance configurations, on which the classical linear discriminant analysis is based, by considering the four models arising from the spectral decomposition when eigenvalues and/or eigenvectors matrices are allowed to vary or not between groups. As in the classical approach, the assessment of these configurations is accomplished via a test on the training set. The discrimination rule is then built upon the configuration provided by the test, considering or not the unlabeled data. Numerical experiments, on simulated and real data, have been performed to evaluate the gain of our proposal with respect to the linear discriminant analysis.     

旅游吸引半径数理模型及实证研究——以水利旅游为例

旅游吸引半径是旅游地与旅游客源市场供求关系的有效边界,而旅游地识别目标客源市场的基础性研究,则是长线型、中线型和短线型旅游战略布局的参考。遵从理论到实证的思路,立足于距离衰减规律和效用论,从旅游吸引力、旅游效用和旅游成本的角度构建旅游吸引半径数理模型,讨论旅游吸引半径有意义的情况;将水利旅游作为实证对象,并引入2004年和2008年的数据,计算中国31个省市自治区的水利旅游吸引半径。研究表明:从时间看,水利旅游吸引半径已经随着时间推移而向外扩展;从空间看,中国江苏、河南等地区的水利旅游吸引半径较大,适宜开发长线型水利旅游客源,而内蒙古、吉林等地区的水利旅游吸引半径较小,仅适宜开发短线型水利旅游客源等。     

Spectral analysis of combustion noise and flame pattern recognition

In many situations, flame patterns in a combustion chamber cannot be observed directly by using an electronic or optical probe. However, an experienced engineer can identify the burning process by listening to the noise that it generates. In this paper, we study acoustic characteristics of turbulent impinging flames by using spectral analysis and statistical pattern recognition. By experimenting with the ignition method, different flame patterns were generated in a laboratory. We find that each flame pattern can be characterized effectively by using the power spectrum of the noise and can be identified by using this information alone.     

面向电子商务企业的物流配送服务半径界定

为界定面向电子商务企业的物流配送服务半径,运用模糊综合评判决策模型,将层次分析法与德尔菲法相结合确定配送企业的综合物流配送能力。通过对“断裂点”公式的修正,对在一定区域内为电子商务企业客户提供配送服务的多个配送企业及其在竞争条件下的服务半径进行了量化界定。分析认为,物流配送服务半径与其综合物流配送能力呈正相关,与竞争对手综合物流配送能力成负相关。     

关于Deutsch定理的注记

本文就任意n阶非负分块矩阵,给出了谱半径的估计公式,推广了Deutsch定理.     

改进运动规律凸轮基圆半径的确定

本文针对凸轮机构推杆作改进梯形加速度、改进正弦加速度和３－４－５次多项式运动规律的情况，研究对心式盘形凸轮机构凸轮基圆半径的确定方法，并利用数值计算方法绘制了基圆半径系数β（ｒ＿０／ｈ）的线图．本文是对已有的用于四种基本运动规律确定基圆半径的诺模图￣［３］和补充诺模图［６］的进一步的发展．