Sphericity Test for High Dimensional Data Based on Random Matrix Theory

In this article we study test of sphericity for high-dimensional covariance matrix in the general population based on random matrix theory. When the sample size is less than data dimension, the classical likelihood ratio test has poor performance for test of sphericity. Thus, we propose a new statistic for test of sphericity by using the higher moments of spectral distribution of the sample covariance matrix, and derive the asymptotic distribution of the statistic under the null hypothesis. Simulation results show that the proposed statistics can effectively improve the power of the test of sphericity for high dimensional data, and have especially significant effects for Spiked model, on the basis of controlling the type-one error probability.     

中草药猫人参与其同科同属植物的光谱分析与鉴别

本文用紫外光谱和荧光光谱等方法对猫人参与其同科同属的木天蓼、藤梨根进行了分析与鉴别。结果表明 :在 2 54nm紫外灯下 ,猫人参水溶液几无荧光 ,而木天蓼、藤梨根水溶液均显较强荧光 ;三种药材提取液的紫外光谱和荧光光谱存在明显差别。     

Propagation of Electromagnetic Waves in Non-Homogeneous Media

We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.     

聚合物表面滴状冷凝传热寿命的实验研究

在滴状冷凝传热寿命测试装置上，对采用离子束动态混合注入（DIMI）技术制备的聚四氟乙烯（PTFE）表面的商状冷凝传热寿命进行了间歇实验测试。满状冷凝已维持约500h（间歇操作总时间为1，000h），实验现象及传热性能趋于基本稳定。同时表明聚合物与金属基体具有较强的结合力。     

Φ630石英轻质抛物面反射镜的二维动态哈特曼检验

简要介绍二维动态哈特曼波前探测仪检测波面形的基本原理、方法及其特点。首次运用该方法对φ630石英轻质抛物面反射镜实现了定量检测，给出了镜面面形测量结果。     

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

1IntroductionTheideaofgeneralizedgrowthcurvemodelsmeanswhereY=(yi,y2,''tAN)isapxNobservationmains;bothBandAarematrixeswithknownconstantelementsoforderpxqandmxNrespectively:(isaqxinparametermatriX;e=(el,ez,'',eN)isarandomerrorrnatrisoforderNxN;Zisanonnegativedefitiveparametermatrixoforderpxp,W=(wij)isaNxNnon-negativedefitivernatriswithknownelements.LetYdenoteamatriXwhosecoluxnnvectorsarethecorrelatedsaxnpleswithsizeNfroma"dimensionalnormalpopulation.Thecovariancematrixofthepopulationis…     

Testing for independence by the empirical characteristic function

Tests of total independence of d (≥2) random variables are proposed using the empirical characteristic function. The approach is parallel to that of Hoeffding, Blum, Kiefer, and Rosenblatt.     

TESTING SPHERICITY IN A GMANOVA-MANOVA MODEL WITH NORMAL ERROR

This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions.     

One‐way analysis of variance with long memory errors and its application to stock return data

Recent empirical results indicate that many financial time series, including stock volatilities, often have long‐range dependencies. Comparing volatilities in stock returns is a crucial part of the risk management of stock investing. This paper proposes two test statistics for testing the equality of mean volatilities of stock returns using the analysis of variance (ANOVA) model with long memory errors. They are modified versions of the ordinary F statistic used in the ANOVA models with independently and identically distributed errors. One has a form of the ordinary F statistic multiplied by a correction factor, which reflects slowly decaying autocorrelations, that is, long‐range dependence. The other is a test statistic such that the degrees of freedom of the denominator in the ordinary F test statistic is calibrated by the so‐called effective sample size. Empirical sizes and powers of the proposed test statistics are examined via Monte Carlo simulation. An application to German stock returns is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Locally minimax tests in symmetrical distributions

In this paper we give an extension of the theory of local minimax property of Giri and Kiefer (1964, Ann. Math. Statist., 35, 21–35) to the family of elliptically symmetric distributions which contains the multivariate normal distribution as a member.This work was partially supported by the Canadian N.S.E.R.C. grant