On tests of symmetry,marginal homogeneity and quasi-symmetry in two-way contingency tables based on minimum φ-divergence estimator with constraints

The restricted minimum φ-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum φ-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221–237], is employed to obtain estimates of the cell frequencies of an I×I contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated φ-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function φ₂ for estimation and the best function φ₁ for testing.     

Testing lack of symmetry in spatial–temporal processes

Symmetry and separability of a covariance function are common assumptions to simplify the modeling effort of spatial–temporal processes. However, many studies in environmental sciences show that real data have complex spatial–temporal dependency structures resulting from lack of symmetry or violation of other standard assumptions of the covariance function. In this study, we propose new formal tests for lack of symmetry by using spectral representations of the spatial–temporal covariance functions of regularly spaced spatial–temporal data. The advantage of the proposed tests is that classical analysis of variance (ANOVA) models can be used for detecting lack of symmetry inherent in spatial–temporal processes. We evaluate the performance of the tests with simulation studies and we apply them to air pollution data.     

甲骨文编码的线性结构

编码是解决甲骨文与计算机"对接"之间矛盾的惟一可行的方法.但目前汉字的编码方式、传统的以部首为主的汉字结构模式和甲骨文"象形"的思维定势难以适应甲骨文编码特点,为此笔者提出甲骨文编码"线性结构"的观点.以甲骨文最小的构形单位"线"以及线与线之间的关系解析甲骨文结构,归纳出独立性、相触性、交叉性和对称性四个甲骨文线性结构特征,作为提取码元之基础,在此基础上形成甲骨文编码方案,码元和键符使用很少,但却能全面涵盖甲骨文字,检索应用起来简单方便.     

词尾标记-e的消失与英语结构对称性破缺

英语词尾-e的逐渐消亡是语言自身通过放大系统中不对称差异,迫使其低维子系统对称破缺,实际上是依靠概念隐喻以牺牲其结构上的对称美来换取话语的经济效率,用经济的话语表达最充分的信息。而语法化是造成语言内部语法标记和结构渐变的重要原因之一。     

A simple test of symmetry about an unknown median

A simple test statistic for testing symmetry of a distribution function about an unknown value is presented. The asymptotic distributions under symmetry and asymmetry are derived. Using the normal as a “calibration” distribution, the critical values of the test are calculated by Monte Carlo methods. Comparisons with other tests indicate that this procedure performs well.     

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.     

Power-divergence-type measure of departure from diagonals-parameter symmetry for square contingency tables with ordered categories

For the analysis of square contingency tables with ordered categories, Goodman considered the diagonals-parameter symmetry (DPS) model. This paper proposes a measure to represent the degree of departure from the DPS model. The proposed measure is expressed by applying Read and Cressie’s power-divergence or Patil and Taillie’s diversity index. The measure would be useful for comparing the degree of departure from the DPS model in several tables. Examples are given.     

Training Intraverbal Naming to Establish Matching-to-Sample Performances

The current study evaluated whether training intraverbal naming would be sufficient to establish visual-visual matching-to-sample (MTS) performances in college students. In the first experiment, we used a multiple-probe design across stimulus sets to assess whether six participants could match arbitrary visual stimuli (AB) after learning to tact their two experimentally defined classes (A’ and B’) and then intraverbally relate their names (i.e., “A’ goes with B’”). All participants matched the stimuli accurately after training, as well as emitted the trained intraverbals. In the second experiment, we used a multiple baseline design across four participants to assess whether the same training would produce bi-directional intraverbals in the form of “B’ goes with A’,” and MTS performance consistent with symmetry (BA). All participants responded accurately during matching and intraverbal tests. Across both experiments, participants stated the trained intraverbals while performing the matching task. Results showed that MTS performance can be established solely by verbal behavior training.     

Conditional symmetry models for three-way contingency tables

We generalize the classical conditional or triangular symmetry model for I×I$I\times I$ contingency tables to three-way I×I×I$I\times I\times I$ tables with commensurable ordinal classification variables. The construction of the new family of models is such that the desirable property that connects conditional symmetry to complete symmetry and marginal homogeneity models in two-way tables is retained in three-way tables. Furthermore, connections between our proposed models obey a coherent structure. We provide maximum likelihood estimation for the new models which is illustrated with a real data example.     

从土中关系看中国的中东政策

中国与阿拉伯国家、伊朗、以色列和土耳其关系是中国中东政策的重点。土耳其和中国在国土面积、资源条件等方面相差很大,但在两国关系上却具有一定的对称性。本文试从经贸发展和国际关系两方面来考察对称性和双边关系之间的相互影响。欧亚大陆,特别是上海合作组织,是密切两国关系最好的平台。建立土中外交轴心有助于消除两国间的分歧与隔阂,推动土中安全领域的合作和中国的中东外交。