Four Correlation Coefficients with a Third Blocking Variable: Their Efficacy,Relative Efficiency,and Test Statistics

Abstract

The efficacy and the asymptotic relative efficiency (ARE) of a weighted sum of Kendall's taus, a weighted sum of Spearman's rhos, a weighted sum of Pearson's r's, and a weighted sum of z-transformation of the Fisher–Yates correlation coefficients, in the presence of a blocking variable, are discussed. The method of selecting the weighting constants that maximize the efficacy of these four correlation coefficients is proposed. The estimate, test statistics and confidence interval of the four correlation coefficients with weights are also developed. To compare the small-sample properties of the four tests, a simulation study is performed. The theoretical and simulated results all prefer the weighted sum of the Pearson correlation coefficients with the optimal weights, as well as the weighted sum of z-transformation of the Fisher–Yates correlation coefficients with the optimal weights.     

Planning for the 1950 Censuses of Population and Agriculture

The change from the z of “Student's” 1908 paper to the t of present day statistical theory and practice is traced and documented. It is shown that the change was brought about by the extension of “Student's” approach, by R.A. Fisher, to a broader class of problems, in response to a direct appeal from “Student” for a solution to one of these problems.     

An Improved Boxplot for Univariate Data

The boxplot is an effective data-visualization tool useful in diverse applications and disciplines. Although more sophisticated graphical methods exist, the boxplot remains relevant due to its simplicity, interpretability, and usefulness, even in the age of big data. This article highlights the origins and developments of the boxplot that is now widely viewed as an industry standard as well as its inherent limitations when dealing with data from skewed distributions, particularly when detecting outliers. The proposed Ratio-Skewed boxplot is shown to be practical and suitable for outlier labeling across several parametric distributions.     

企业非确定型决策与中庸

在企业常用的非确定型决策方法中 ,决策者对未来所持的态度不同 ,选择的方案就不同。如何保持正常的心态 ,作出科学的选择 ,这一思想正好与中国传统文化中道德领域的中庸相一致。中庸强调“既不太过 ,也不不及” ,保持“适中”的人生态度。古为今用 ,不同领域 ,问题的根本都是对不确定型问题的决策     

从解一个古典概率问题所想到的

文章给出一个古典概率问题的两个解法，从而导出几个有趣的等式。     

产品品种繁多类型企业投入产出表的处理思想与方法

对于生产装配性产品的机械企业，由于产品与原材料种类繁多，将造成企业投入产出表的规模庞大，致使投入产出表的编制、计算和使用产生诸多问题，甚至难以实现。为了控制表的规模，常采用将消耗量相近、生产工艺相近的产品合并的做法。但这种做法严重影响了投入产出表的精度和应用效果。因此，本文讨论了更为有效的解决这类问题的思想和方法。     

Semiparametric Inference Methods for General Time Scale Models

In this paper we consider semiparametric inference methods for the time scale parameters in general time scale models (Oakes, 1995, Duchesne and Lawless, 2000). We use the results of Robins and Tsiatis (1992) and Lin and Ying (1995) to derive a rank-based estimator that is more efficient and robust than the traditional minimum coefficient of variation (min CV) estimator of Kordonsky and Gerstbakh (1993) for many underlying models. Moreover, our estimator can readily handle censored samples, which is not the case with the min CV method.     

城乡居民收入差距不合理因素分析及对策

城镇居民和农村居民的收入差距发生了本质变化城乡居民的显性收入差距不能确切反映实际收入差距;差距悬殊而且存在着非自然差距;超过了世界各国相同阶段所固有的水平;收入差距处在倒"U"型曲线的上升阶段.为缩小城乡居民收入差距,必须增加土地投资;保护和提高农民生产的积极性;进行农业产业结构调整;优化农村政策结构;发展教育,培养专业技术人才,加快贫困地区文化、技术和制度等资源开发;实现农业劳动力半转移.     

A Goodness-of-Fit Test for Location-Scale Max-Stable Distributions

In this article, a technique based on the sample correlation coefficient to construct goodness-of-fit tests for max-stable distributions with unknown location and scale parameters and finite second moment is proposed. Specific details to test for the Gumbel distribution are given, including critical values for small sample sizes as well as approximate critical values for larger sample sizes by using normal quantiles. A comparison by Monte Carlo simulation shows that the proposed test for the Gumbel hypothesis is substantially more powerful than some other known tests against some alternative distributions with positive skewness coefficient.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.