Testing equality of two normal covariance matrices with monotone missing data

Abstract

The problem of testing equality of two multivariate normal covariance matrices is considered. Assuming that the incomplete data are of monotone pattern, a quantity similar to the Likelihood Ratio Test Statistic is proposed. A satisfactory approximation to the distribution of the quantity is derived. Hypothesis testing based on the approximate distribution is outlined. The merits of the test are investigated using Monte Carlo simulation. Monte Carlo studies indicate that the test is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example.     

Heteroscedastic Global Tests that the Regression Parameters for Two or More Independent Groups are Identical

Simulation results are reported on methods that allow both within group and between group heteroscedasticity when testing the hypothesis that independent groups have identical regression parameters. The methods are based on a combination of extant techniques, but their finite-sample properties have not been studied. Included are results on the impact of removing all leverage points or just bad leverage points. The method used to identify leverage points can be important and can improve control over the Type I error probability. Results are illustrated using data from the Well Elderly II study.     

几类全微分方程问题的求解定理

利用全微分方程的条件，给出一类微分方程的积分因子及通解公式，得出一类全微分方程中未知函数所满足的二阶线性微分方程，获得未知函数及全微分方程的通解。     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

Estimator Choice and Fisher's Paradox: A Monte Carlo Study

This paper argues that Fisher's paradox can be explained away in terms of estimator choice. We analyse by means of Monte Carlo experiments the small sample properties of a large set of estimators (including virtually all available single-equation estimators), and compute the critical values based on the empirical distributions of the t-statistics, for a variety of Data Generation Processes (DGPs), allowing for structural breaks, ARCH effects etc. We show that precisely the estimators most commonly used in the literature, namely OLS, Dynamic OLS (DOLS) and non-prewhitened FMLS, have the worst performance in small samples, and produce rejections of the Fisher hypothesis. If one employs the estimators with the most desirable properties (i.e., the smallest downward bias and the minimum shift in the distribution of the associated t-statistics), or if one uses the empirical critical values, the evidence based on US data is strongly supportive of the Fisher relation, consistently with many theoretical models.     

低浓度三分子反应模型双曲型反应－扩散方程的稳定性与化学振荡

考虑浓度扩散和扩散流随时间的变化，得到低浓度三分子反应模型的双曲型反应－扩散方程；讨论了方程的稳定性及存在行波解的条件，得到了化学振荡的色散关系和相速度．     

将分段函数表示为初等函数的方法

本文给出了一种化具有多个分段点，且在各区间段上的表达式为多项式函数的分段函数为初等函数的具体方法．     

二阶非线性微分方程解的振动性和渐近性

讨论了二阶非线性常微分方程(α(t)(?)(x)x′)′+q(t)f(x)=r(t)的解的振动性和渐近性.获得了有关该方程的五个新的定理.     

Some remarks on the physical models concerning two different approaches to inference in statistical process control

Summary For technological applications it can be useful to identify some simple physical mechanisms, which, on the basis of the available knowledge of the production process, may suggest the most appropriate approach to statistical control of the random quantities of interest. For this purpose the notion of rupture point is introduced firstly. A rupture point is characterized bym randomly arising out of control states, assumed to be mutually exclusive and stochastically independent. Shewhart's control charts seem to represent the natural statistical tool for controlling a rupture point; however it is shown that they are fully justified only when the hazard rates attached to the causes of failure are constant. Otherwise, typically in the presence of time increasing hazard rates, Shewhart's control charts should be completed by a preventive intervention rule (preventive maintenance). In the second place, the notion of dynamic instability point is introduced, which is specifically characterized by assuming that the random quantity of interest is ruled by a stochastic differential equation with constant coefficients. By discretization, developed according to a possibly new approach, it is shown that the former model reduces to an equation error model, which is among the simplest used in adaptive control, and thus particularly easy to deal with in regard to parameter estimation and the definition of the optimum control rule.     

变质量任意阶非线性非完整系统的相对论性广义Mac-Millan型方程

提出了变质量系统的相对论性万有D’Alembert原理,构造了相对论性广义动能函数,建立了变质量任意阶非线性非完整系统在准坐标下和广义坐标下的相对论性广义Mar-Millan型方程,并得到厂相应的型方程