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…     

An examination of the correlation between earthquake, positions of solar system bodies and solid tide

After processing 204 data of historical earthquakes for M ⩾ 4.5 from 1900 to 1996 in the area centered at Beijing (39.9°N, 116.4° E; ±3°), two correlations have been suggested: One is between earthquake and the position distribution of major solar system bodies; the other is between the earthquake magnitude and the tidal force at the epicenter. A tentative is presented for future seism prediction. Because this work is at the test stage based on a statistic analysis, further test and verification are expected.     

Some test statistics based on the martingale term of the empirical distribution function

Summary It is proved that the martingale term of the empirical distribution function converges weakly to a Gaussian process inD[0, 1]. Some statistics for goodness-of-fit tests based on the martingale term of the empirical distribution function are proposed. Asymptotic distributions of these statistics under the null hypothesis are given. The approximate Bahadur efficiencies of the statistics to the Kolmogorov-Smirnov statistic and to the Cramér-von Mises statistic are also calculated. The Institute of Statistical Mathematics     

投资环境地区横向比较

本文以各地区经济数据为基础,通过建立统计分析的数学模型,给出了度量、评测投资环境的客观标准,并应该标准对几个典型城投资环境进行评价和分类,从一个新的角度,就客观、定量的研究投资环境进行了探索.     

Exponential stability of singularly perturbed impulsive delay differential equations

In this paper, the exponential stability of singularly perturbed impulsive delay differential equations (SPIDDEs) is concerned. We first establish a delay differential inequality, which is useful to deal with the stability of SPIDDEs, and then by the obtained inequality, a sufficient condition is provided to ensure that any solution of SPIDDEs is exponentially stable for sufficiently small ε>0. A numerical example and the simulation result show the effectiveness of our theoretical result.     

市场竞争条件下统计熵的性质与分析

人们对市场竞争状态的描述，大多从微观角度出发，研究微观主体自身在市场竞争中的地位和变化状态，本文从宏观角度出发，定义统计熵的性质和数学公式，从数学上证明统计熵的取值特征，进而分析出统计熵取值与市场竞争的关系，这种质量描述可为政府进行宏观调控，维持较好的市场结构提供科学依据。     

Asymptotic normality of double-indexed linear permutation statistics

The paper provides sufficient conditions for the asymptotic normality of statistics of the form a _ijb_RiRj, wherea _ijandb _ijare real numbers andR _iis a random permutation.     

材料组成特性的统计表征--原位统计分布分析

提出了原位统计分布分析的新概念，它以测试信息原位性、原始性、统计性为特征，旨在反映材料中较大尺度（cm^2）范围内不同组成的定量统计分布规律，系现有宏观平均含量分析及微观结构分析之外的另一种材料性能表征的技术。以火花光谱无预燃单次放电（SDA）、连续激发及高速采集解析技术为基础，研制了金属材料原位分析仪。火花光谱单次放电（SDA）研究指出，在无预燃的情况下，每一个火花单次放电的信号都与该材料对应位置及原始状态相关。当对材料在较大尺度范围内，实现无预燃激发时，则可以获得几万个、几十万、乃至几百万个单次放电的信号，它们分别与各自放电的原始位置厦原始状态相对应。在信号统计解析的基础上，提出了一些表征材料性状的新信息，如在材料中，各元素不同位置含量的统计定量分布；各元素偏析度的准确定量计算；元素不同含量在材料中所占的原位（置）权重比率（统计偏析度）；统计致密度；夹杂物及粒度的统计定量分布等．该技术成功地应用于连铸等冶金工艺、材料研究及生产的质量判据。     

New permutation statistics: Variation and a variant

For each permutation π we introduce the variation statistic of π, as the total number of elements on the right between each two adjacent elements of π. We modify this new statistic to get a slightly different variant, which behaves more closely like Mahonian statistics such as maj. In this paper we find an explicit formula for the generating function for the number of permutations of length n according to the variation statistic, and for that according to the modified version.     

A semiparametric Wald statistic for testing logistic regression models based on case-control data

We propose a semiparametric Wald statistic to test the validity of logistic regression models based on case-control data. The test statistic is constructed using a semiparametric ROC curve estimator and a nonparametric ROC curve estimator. The statistic has an asymptotic chisquared distribution and is an alternative to the Kolmogorov-Smirnov-type statistic proposed by Qin and Zhang in 1997, the chi-squared-type statistic proposed by Zhang in 1999 and the information matrix test statistic proposed by Zhang in 2001. The statistic is easy to compute in the sense that it requires none of the following methods: using a bootstrap method to find its critical values, partitioning the sample data or inverting a high-dimensional matrix. We present some results on simulation and on analysis of two real examples. Moreover, we discuss how to extend our statistic to a family of statistics and how to construct its Kolmogorov-Smirnov counterpart. This work was supported by the 11.5 Natural Scientific Plan (Grant No. 2006BAD09A04) and Nanjing University Start Fund (Grant No. 020822410110)