Testing Symmetry of the Error Distribution in Nonlinear Heteroscedastic Models

Using the empirical characteristic function, we derive a Cramér-von Mises test for symmetry of the error distribution in a class of nonlinear parametric heteroscedastic models. We study the convergence of the residual-based empirical distribution function. We establish a functional limit theorem for an empirical process of residuals, and investigate the asymptotic null distribution function of our test statistic. A simulation experiment is conducted to evaluate small-sample performances of our test.     

Two new estimators of entropy for testing normality

ABSTRACT

We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the existing entropy estimators. Also, we propose two new tests for normality based on the introduced entropy estimators and compare their powers with the powers of other tests for normality. The results show that the proposed estimators and test statistics perform very well in estimating entropy and testing normality. A real example is presented and analyzed.     

Discrete adaptive design in attribute life testing

Properties of a discrete adaptive design in attribute life testing situation are studied. It is shown that the design is strongly consistent and asymptotically normal. Some examples are discussed to show that the design could be used in a wide range of ields, Finally, we give some simulation results to compare the discrete adaptive desigin with some continuous optimal designs.     

The robustness of point optimal testing for rosenberg random regression coefficients

The literature on testing for the presence of Rosenberg's (1973) return to normalcy random coefficient model is well developed with both Shively (1988) and Brooks (1993) advocating the use of point optimal tests. This paper explores the robustness of point optimal testing for the Rosenberg alternative to two departures: the special case HildrethHouck (1968) alternative and non-normality in regression disturbances, finding the point optimal testing approach to be fairly robust to both departures.     

Simulation Study on Improved Shapiro–Wilk Tests for Normality

The article concerns tests for normality based on the Shapiro–Wilk W statistic. The constants in the test statistic are recalculated as those given in Shapiro and Wilk are incorrect. The empirical significance levels and power of improved tests have been evaluated in simulation study and compared to original ones. The improved tests were also applied to the multivariate case. In this case, we consider two implementations of the W statistic, the first one proposed by Srivastava and Hui and the other by Hanusz and Tarasinska. Empirical size of tests and their power have been compared to the Henze–Zirkler test.     

Testing Variability in the Two-Sample Case

A number of robust methods for testing variability have been reported in previous literature. An examination of these procedures for a wide variety of populations confirms their general robustness. Shoemaker's improvement of the F test extends that test use to a realistic variety of population shapes. However, a combination of the Brown–Forsythe and O'Brien methods based on testing kurtosis is shown to be conservative for a wide range of sample sizes and population distributions. The composite test is also shown to be more powerful in most conditions than other conservative procedures.     

An Exponential Model for Damage Accumulation

In this article, we present a general model for predicting the fatigue behavior for any stress level and amplitude using the exponential model. Based on the Wöhler field for fixed stress level, a compatibility functional equation enables us to derive the general model with eight parameters. The problem of parameter estimation is then discussed and some methods are described. Some examples are finally presented to illustrate the derived model and the proposed methods of estimation.     

Discreteness Causes Bias in Percentage-Based Comparisons: A Case Study From Educational Testing

Discretizing continuous distributions can lead to bias in parameter estimates. We present a case study from educational testing that illustrates dramatic consequences of discreteness when discretizing partitions differ across distributions. The percentage of test takers who score above a certain cutoff score (percent above cutoff, or “PAC”) often describes overall performance on a test. Year-over-year changes in PAC, or ΔPAC, have gained prominence under recent U.S. education policies, with public schools facing sanctions if they fail to meet PAC targets. In this article, we describe how test score distributions act as continuous distributions that are discretized inconsistently over time. We show that this can propagate considerable bias to PAC trends, where positive ΔPACs appear negative, and vice versa, for a substantial number of actual tests. A simple model shows that this bias applies to any comparison of PAC statistics in which values for one distribution are discretized differently from values for the other.     

A Goodness-of-fit Test for Exponentiality Based on the Memoryless Property

In this investigation a test of goodness of fit for exponentiality is proposed. This procedure applies equally whether the scale and/or the location parameters of the distribution are known or not. The limiting null and non-null distributions of the test statistic are normal under minimal conditions. Monte Carlo critical values for small sample sizes are given and the power of the test is calculated for various alternatives showing that it compares favourably relatively to other more complicated published procedures.     

大学英语四、六级网络考试考场建设研究

大学英语四、六级网考项目开始于2007年,第一次四级网考试点工作实施于2008年12月。大学英语四、六级网考项目的建设目标,是提高大学英语四、六级考试的效度和考务管理效率。以2009年10月份的一次考试为例,描述CET-4大学英语网考考场内的硬件设置、环境设置、网考所需的软件、硬件配置和考试系统的操作流程,并且对网考中出现的问题进行剖析,有助于提出行之有效的改进方案。