双参数指数分布位置参数的统计推断

通过次序统计量,得到了双参数指数分布Ｅ（μ,λ）中位置参数μ的一致最小方差无偏估计为ｎｎ－１Ｔ（１）－１ｎ－１Ｔ＾－,推导出了（Ｔ＾＿－μ）／Ｔ＾－－Ｔ（１））的分布与参数μ,λ无关,从而得到了μ的置信区间与检验统计量。     

参数模型下的时间序贯检验方案

本文研究参数模型下的序贯检验方案 .而以往的序贯检验方案往往采取非参数模型 .由于参数模型在生产实践中是常见的形式 .所以这个检验方案对于产品的检验具有指导意义 .     

双参数指数分布尺度参数变化幅度的区间估计

本文将Ｓｃｈｅｃｈｔｍａｎ（１９８３）文中的方法加以修改后应用到双参数指数分布尺度参数变化幅度ρ的估计上，得到了一个保守的置信下限，并通过随机模拟证明了这个置信下限不是平凡的。     

双参数13参四边形板元

本文提出了一个双参数13参四边形板元, 其中一套参数按照广义分片检验要求选取, 另一套真正节点参数按照使离散系统更易解的要求选取,通过数值方法将一套节点参数线性过渡到另一套, 并且证明了该元的收敛性, 给出算例加以验证.     

随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

双参数指数分布环境因子的Bayes估计

讨论了定数截尾样本下双参数指数分布环境因子的极大似然估计、区间估计和Bayes估计.以参数后验密度的商密度作为环境因子的后验密度,并结合专家经验运用Bayes方法给出了环境因子在平方损失下和LINEX损失下的Bayes估计.最后运用Monte Carlo方法对各估计结果的均方误差(MSE),进行了模拟比较.结果表明LINEX损失下环境因子的估计较好.     

双参数指数截尾分布参数估计相合性的证明

给出了双参数指数分布截尾寿命试验样本的联合分布,得到了参数的极大似然估计,并证明了该估计的相合性.     

多个Panel数据模型回归系数的参数Bootstrap检验

对多个只含有个体效应的Panel数据模型,研究了模型中回归系数向量相等性的假设检验问题,提出了一种参数Bootstrap检验方法.有限样本的数值模拟研究结果表明,提出的检验方法具有良好.的检验功效,且受个体效应方差、误差方差、模型个数、回归系数维数的影响不明显.     

定时截尾场合下双参数指数分布的参数估计

本文给出了定量截尾场合下双参数指数分布中两个参数的近似无偏估计（AUE），计算了它们的期望及方差，并与极大似然估计，相应定数截尾场合下的估计做了比较。     

A Partial Empirical Likelihood Based Score Test Under a Semiparametric Finite Mixture Model

We propose a score statistic to test the null hypothesis that the two-component density functions are equal under a semiparametric finite mixture model. The proposed score test is based on a partial empirical likelihood function under an I-sample semiparametric model. The proposed score statistic has an asymptotic chi-squared distribution under the null hypothesis and an asymptotic noncentral chi-squared distribution under local alternatives to the null hypothesis. Moreover, we show that the proposed score test is asymptotically equivalent to a partial empirical likelihood ratio test and a Wald test. We present some results on a simulation study.     

QNQL过程在排队论中的应用（Ⅰ）：输入过程（独立同分布情形）

本文在“相邻两个顾客到达时间间隔独立同分布”这个假定下，讨论输入过程Ｎ（ｔ）的拉氏变换及概率分布问题．     

Testing goodness of fit for the distribution of errors in multivariate linear models

In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.     

The likelihood ratio criterion and the asymptotic expansion of its distribution

Summary Asymptotic expansion of the distribution of the likelihood ratio criterion (LRC) for testing a composite hypothesis is derived under null hypothesis and a correction factor ρ which makes the term of order 1/n in the asymptotic expansion of the distribution of it vanish is obtained. The problem is extended to the case of a general composite hypothesis and of Pitman's local alternatives. The asymptotic distribution of LRC for a simple hypothesis is studied under a fixed alternative. The Institute of Statistical Mathematics     

A note on testing hypotheses for stationary processes in the frequency domain

In a recent paper, Eichler (2008) [11] considered a class of non- and semiparametric hypotheses in multivariate stationary processes, which are characterized by a functional of the spectral density matrix. The corresponding statistics are obtained using kernel estimates for the spectral distribution and are asymptotically normally distributed under the null hypothesis and local alternatives. In this paper, we derive the asymptotic properties of these test statistics under fixed alternatives. In particular, we also show weak convergence but with a different rate compared to the null hypothesis. We also discuss potential statistical applications of the asymptotic theory by means of a small simulation study.     

Hypothesis testing for the generalized multivariate modified Bessel model

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T²-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T²-statistic for the Behrens–Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model.     

利用有限局部环Z/pkZ上的幂等矩阵的标准型构作认证码

In this paper,we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p~kZ,from which we construct a Cartesian au- thentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.     

Using Normal Form of Idempotent Matrices over Finite Local Ring Z/p^kZ to Construct Cartesian Authentication Codes

In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.     

Approximation by randomly weighting method in censored regression model

Censored regression (“Tobit”) models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the performance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis. This work was supported by National Natural Science Foundation of China (Grant No. 10471136), PhD Program Foundation of the Ministry of Education of China, and Special Foundations of the Chinese Academy of Sciences and University of Science and Technology of China     

A test for elliptical symmetry

This paper presents a statistic for testing the hypothesis of elliptical symmetry. The statistic also provides a specialized test of multivariate normality. We obtain the asymptotic distribution of this statistic under the null hypothesis of multivariate normality, and give a bootstrapping procedure for approximating the null distribution of the statistic under an arbitrary elliptically symmetric distribution. We present simulation results to examine the accuracy of the asymptotic distribution and the performance of the bootstrapping procedure. Finally, for selected alternatives, we compare the power of our test statistic with that of recently proposed tests for elliptical symmetry given by Manzotti et al. [A statistic for testing the null hypothesis of elliptical symmetry, J. Multivariate Anal. 81 (2002) 274-285] and Schott [Testing for elliptical symmetry in covariance-matrix-based analyses, Statist. Probab. Lett. 60 (2002) 395-404], and with that of the well known tests for multivariate normality of Mardia [Measures of multivariate skewness and kurtosis with applications, Biometrika 57 (1970) 519-530] and Baringhaus and Henze [A consistent test for multivariate normality based on the empirical characteristic function, Metrika 35 (1988) 339-348].