A modified Kolmogorov-Smirnov test for a rectangular distribution with unknown parameters: Computation of the distribution of the test statistic

A recursive scheme for the calculation of the distribution of the test statistic of a modified Kolmogorov-Smirnov-test for a rectangular distribution with unknown parameters is given.     

Distance sampling methodology

We consider the method of distance sampling described by Buckland, Anderson, Burnham and Laake in 1993. We explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design- and model-based frameworks. In particular, we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator within each framework. These results enable us to clarify aspects of the performance of the methodology which may be of interest to users and potential users of distance sampling.     

Saddlepoint-Based Bootstrap Inference for Quadratic Estimating Equations

Abstract.  We propose an easy to implement method for making small sample parametric inference about the root of an estimating equation expressible as a quadratic form in normal random variables. It is based on saddlepoint approximations to the distribution of the estimating equation whose unique root is a parameter's maximum likelihood estimator (MLE), while substituting conditional MLEs for the remaining (nuisance) parameters. Monotoncity of the estimating equation in its parameter argument enables us to relate these approximations to those for the estimator of interest. The proposed method is equivalent to a parametric bootstrap percentile approach where Monte Carlo simulation is replaced by saddlepoint approximation. It finds applications in many areas of statistics including, nonlinear regression, time series analysis, inference on ratios of regression parameters in linear models and calibration. We demonstrate the method in the context of some classical examples from nonlinear regression models and ratios of regression parameter problems. Simulation results for these show that the proposed method, apart from being generally easier to implement, yields confidence intervals with lengths and coverage probabilities that compare favourably with those obtained from several competing methods proposed in the literature over the past half-century.     

Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs

In this paper we consider the problem of estimating a coefficient of a strongly elliptic partial differential operator in stochastic parabolic equations. The coefficient is a bounded function of time. We compute the maximum likelihood estimate of the function on an approximating space (sieve) using a finite number of the spatial Fourier coefficients of the solution and establish conditions that guarantee consistency and asymptotic normality of the resulting estimate as the number of the coefficients increases. The equation is assumed diagonalizable in the sense that all the operators have a common system of eigenfunctions.     

普通高校足球选项课考核研究

运用文献资料法、教学实验法，对学生进行测试、分析。结果表明，实验所选考核内容在理论上被证实并且对学生有较强适用性，方法上可分别量化，操作简便，评分符合正态分布理论。     

Group sequential x2 statistic for testing the difference of two mean vectors in clinical trials

In this study we discuss the group sequential procedures for comparing two treatments based on multivariate observations in clinical trials. Also we suppose that a response vector on each of two treatments has a multivariate normal distribution with unknown covariance matrix. Then we propose a group sequential x² statistic in order to carry out repeated significance test for hypothesis of no difference between two population mean vectors. In order to realize the group sequential test where average sample number is reduced, we propose another modified group sequential x² statistic by extension of Jennison and Turnbull ( 1991 ). After construction of repeated confidence boundaries for making the repeated significance test, we compare two group sequential procedures based on two statistics regarding the average sample number and the power of the test in the simulations.     

An exact test for nbue class of survival functions

Let F(x) be a life distribution. An exact test is given for testing H₀ F is exponential, versusH₁Fε NBUE (NWUE); along with a table of critical values for n=5(l)80, and n=80(5)65. An asymptotic test is made available for large values of n, where the standardized normal table can be used for testing.     

面向二十一世纪高校德育的出路

本文从当前高校德育教育的现状及存在问题 ,分析 2 1世纪高校德育教育的出路。     

理学统治地位的确立与元中期学风的转变

元代中叶科举考试的恢复，奠定了程朱理学的统治地位，从而引起了元代中期学术风气的变 化，这种变化主要有三个特点，即趋于正、趋于实、趋于古。这种学风，对元中期雅正文学 思潮的形成产生重大影响。     

电子回旋共振放电中电子能量分布特性的研究

建立了电子回旋共振(ECR)放电的粒子模型,编制了准三维电磁模粒子模拟与蒙特卡罗模拟程序。通过对氩气ECR放电电离过程的理论分析与数值模拟,得到了放电稳态形成时不同放电区域的电子能量分布。研究了不同中性气压以及外加磁场位形对这些区域中电子能量分布特性的影响。随着中性气压的升高,远离ECR区域中的低能电子减少,高能电子增加,而ECR区域中电子能量分布变化特征与之相反;相对于收敛磁场位形,磁镜磁场位形更有利于约束放电下游区的电子能量以及电子能量分布的宽度。