Detecting Randomness: A Review of Existing Tests with New Comparisons

In this article we review and compare a number of existing tests for detecting randomness in time series data, with emphasis on stock market index data. By comparing variance ratio tests with traditional statistical tests, we have the most extensive simulation comparison of such procedures. The investigated tests are compared over a diverse group of distributions, models, and stock market applications. In our stock market data analysis, the choice of data transformation can have a noticeable effect on test results. This study provides the reader with a guide as to which test and transformation is most appropriate for their use.     

Confessions of a Coin Flipper and Would-Be Instructor

Simulation data are used to test a student's beliefs about the relative probabilities of two sequences obtained by flipping a fair coin. The episode is used to illustrate general issues in using simulations instructionally.     

即时计算机辅助会话语言性别差异研究的新方法

即时计算机辅助会话正极大地改变着人类语言生活的面貌,对其中语言性别差异的研究有利于理解计算机辅助会话影响人类语言的范围和机制,也为重新认识现有语言性别差异理论提供重要依据。但现有研究还存在抽样随机性不足、数据分析方法不当等问题,严重地影响了研究结论的信度。鉴于此,有必要在研究中引入新方法,在保证抽样随机性的基础上,根据数据测量类型和变量性质采用卡方检验来推断某一语言变量性别差异的显著性,重新全面审视现有研究的结论。     

Testing Chaos Based on Empirical Distribution Function: A Simulation Study

It is well known that many classical statistical tests of randomness generally fail to distinguish chaos generated by some lower-dimensional deterministic dynamical systems from independent and identically distributed (i.i.d.) random series. In this paper, we suggest a powerful statistical testing method based on empirical distribution function that can well detect chaos and i.i.d. random series.     

生物种群空间格局随机性的一个检验方法

以最近邻体法的调查为基础，提出一种检验生物种群空间格局随机性的方法，其理论基础是DeMoivre-Laplace中心的极限定理。     

Sample Entropy Statistics and Testing for Order in Complex Physiological Signals

Sample Entropy (SampEn) statistics have provided insight into the amount of order present in several types of complex physiological time series, particularly the heart rate dynamics of premature infants. Very little, however, is known of SampEn's statistical properties and this has hindered strategies for optimization and significance testing. This article shows that SampEn statistics are asymptotically Gaussian under general conditions. A straightforward point estimate of the statistic's variance is developed and compared to empirical results obtained from complex surrogate data. Statistical tests are developed to quantify the amount and scale of order detected in a signal. These tests are used to show that significant order is, in fact, being detected in the heart rate dynamics of neonates, and to suggest strategies for optimizing the analysis parameters.     

抽样调查下样本随机性的检验

 抽样调查下样本随机性的检验,不是考查抽样方法的优劣或是检查样本代表性的好坏,而是为了控制抽样调查的数据质量,检验所得样本和抽样方法的一致性,即调查机构是否严格按照抽样设计的要求去抽取样本。本文以等概率和不等概率抽样为例,揭示了如何利用相关辅助信息,构造检验统计量,进行样本随机性的检验。     

Testing multivariate uniformity: The distance‐to‐boundary method

Given a random sample taken on a compact domain S ? ^d, the authors propose a new method for testing the hypothesis of uniformity of the underlying distribution. The test statistic is based on the distance of every observation to the boundary of S. The proposed test has a number of interesting properties. In particular, it is feasible and particularly suitable for high dimensional data; it is distribution free for a wide range of choices of 5; it can be adapted to the case that the support of S is unknown; and it also allows for one‐sided versions. Moreover, the results suggest that, in some cases, this procedure does not suffer from the well‐known curse of dimensionality. The authors study the properties of this test from both a theoretical and practical point of view. In particular, an extensive Monte Carlo simulation study allows them to compare their methods with some alternative procedures. They conclude that the proposed test provides quite a satisfactory balance between power, computational simplicity, and adaptability to different dimensions and supports.