Multivariate analysis with an autoregressive covariance model

This paper addresses the problem of testing the multivariate linear hypothesis when the errors follow an antedependence model (Gabriel, 1961, 1962). Antedependence can be formulated as a nonstationary autoregressive model of general order. Three test statistics are derived that provide analogs to three commonly used MANOVA statistics: Wilks' Lambda, the Lawley-Hotelling Trace, and Pillai's Trace. Formulas are given for each of these statistics that show how they can be obtained From any statistical computing package that calculates the usual MANOVA statistics. These antedependent statistics would be appropriate in analyzing certain multivariate data sets in which repeated measurements are taken on the same subjects over a period of time.     

Enhancing statistical education by using role-plays of consultations

Summary.  Role-plays in which students act as clients and statistical consultants to each other in pairs have proved to be an effective class exercise. As well as helping to teach statistical methodology, they are effective at encouraging statistical thinking, problem solving, the use of context in applied statistical problems and improving attitudes towards statistics and the statistics profession. Furthermore, they are fun. This paper explores the advantages of using role-plays and provides some empirical evidence supporting their success. The paper argues that there is a place for teaching statistical consulting skills well before the traditional post-graduate qualification in statistics, including to school students with no knowledge of techniques in statistical inference.     

Some Characterizations Based on Entropy of Order Statistics and Record Values

In the literature of information theory, Shannon entropy plays an important role and in the context of reliability theory, order statistics and record values are used for statistical modeling. The aim of this article is characterizing the parent distributions based on Shannon entropy of order statistics and record values. It is shown that the equality of the Shannon information in order statistics or record values can determine uniquely the parent distribution. The exponential distribution is characterized through maximizing Shannon entropy of record values under some constraints. The results are useful in the modeling problems.     

Two-Term Edgeworth Expansions for the Classes of U- and V-statistics

Much effort has been devoted to deriving Edgeworth expansions for various classes of statistics that are asymptotically normally distributed, with derivations tailored to the individual structure of each class. Expansions with smaller error rates are needed for more accurate statistical inference. Two such Edgeworth expansions are derived analytically in this paper. One is a two-term expansion for the standardized U-statistic of order m, m ? 3, with an error rate o(n^{? 1}). The other is an expansion with the same error rate for the distribution of the standardized V-statistic of the same order. In deriving the Edgeworth expansion, we made use of the close connection between the V- and U-statistics, which permits to first derive the needed expansion for the related U-statistic, then extend it to the V-statistic, taking into consideration the estimation of all difference terms between the two statistics.     

统计数据开发的混沌思考

 统计学是研究随机现象统计规律性的学科。贝叶斯学派认为是：“以样本推断总体的艺术”。统计数据作为样本的数量反映,同时具有随机性和确定性的双重意义。混沌则是“确定性的随机性”（福特语）,“是有序与无序都很强烈时形成的动力学”（苗东升语）。可见,统计学与混沌学有着天然的“缘分”,本文呼唤统计学界同仁,注意到如下实际：混沌理论的创立,是继相对论和量子力学问世以来,对人类整个知识体系的又一次巨大冲击,是20世纪数理科学的第三次革命,正如格莱克在他的《混沌：开创新学科》一书中所说：“混沌开始之处,经典科学就终止了”。在统计分析中,特别是数据开发时应留给混沌理论一定的空间。、     

The Scaled Uniform Model Revisited

Abstract

Sufficiency, conditionality, and invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to teach modern methods. However, being the philosophical cornerstones of statistical inference, a minimal understanding of these principles should be part of any curriculum in statistics. The scaled uniform model is used here to demonstrate the importance and usefulness of the conditionality principle, which is probably the most basic and less familiar among the three.     

Non-parametric predictive inference for future order statistics

This article presents non-parametric predictive inference for future order statistics. Given the data consisting of n real-valued observations, m future observations are considered and predictive probabilities are presented for the rth-ordered future observation. In addition, joint and conditional probabilities for events involving multiple future order statistics are presented. The article further presents the use of such predictive probabilities for order statistics in statistical inference, in particular considering pairwise and multiple comparisons based on two or more independent groups of data.     

An Estimator of Shannon Entropy of Beta-Generated Distributions and a Goodness-of-Fit Test

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek’s estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives.     

Reliability properties of record values from non-identically distributed random variables

In reliability theory, order statistics and record values are used for statistical modelling. The r-th order statistic in a sample of size n represents the life—length of a (n?r+l)-out-of-n system, and record values are used in shock models. In recent years, reliability properties of order statistics and record values have been investigated. The two models are included in Pfeifer's concept of record values from non-identically distributed random variables. Here, some results on the transmission of distributional properties, such as increasing failure rate, are shown for such records, which contain the results for order statistics and ordinary record values as particular cases.     

国际贸易统计研究中的几个基本关系

为使国际贸易统计和贸易平衡的研究更为深入和更好地开展,本文建议在研究中要处理好以下三个基本关系：经济发展与统计体系建设的关系,中国贸易统计的国际接轨与促进国际统计制度变革的关系,贸易统计数据生产与贸易统计数据使用的关系。     

Powerful nonparametric statistics to compare k independent ROC curves

The authors deal with the problem of comparing receiver operating characteristic (ROC) curves from independent samples. From a nonparametric approach, they propose and study three different statistics. Their asymptotic distributions are obtained and a resample plan is considered. In order to study the statistical power of the introduced statistics, a simulation study is carried out. The (observed) results suggest that, for the considered models, the new statistics are more powerful than the usually employed ones (the Venkatraman test and the usual area under the ROC curve criterion) in non-uniform dominance situations and quite good otherwise.     

对应分析统计检验体系探讨

对应分析因其结果的易读性，近些年得到了越来越广泛的应用。为了更好地应用对应分析，提出建立对应分析统计检验体系，包括对应分析适用性的统计检验以及对应分析效果的检验，同时还提出应用对应分析时应注意的其它问题。     

Some Remarks on Statistical Education

A definition of the subject of statistics is given, and the difference between the chalkboard world of the teacher of statistics and the real world of the experimenter is stressed. An overemphasis on significance testing, hypothesis testing, and decision procedures has led to a de-emphasis of statistical design. The teaching of statistical design theory, statistics teaching in a changing world, the importance of model building, and different approaches to teaching statistics are discussed. Some published materials developed to meet teaching needs and a new type of statistics course are described. Information about special issues in statistical education (teaching and consulting) is presented.     

Comparison among non parametric prediction intervals of order statistics

Abstract

In this article, we are interested in conducting a comparison study between different non parametric prediction intervals of order statistics from a future sample based on an observed order statistics. Typically, coverage probabilities of well-known non parametric prediction intervals may not reach the preassigned probability levels. Moreover, prediction intervals for predicting future order statistics are no longer available in some cases. For this, we propose different methods involving random indices and fractional order statistics. In each case, we find the optimal prediction intervals. Numerical computations are presented to assess the performances of the so-obtained intervals. Finally, a real-life data set is presented and analyzed for illustrative purposes.     

会计与统计的相互借鉴及相关思考

1992年国民经济核算体系的推广和1993年会计制度的改革几乎同时并举,使宏观统计核算和微观会计核算有了进一步交流和相互借鉴的可能。 近几年来,统计学界对统计核算借鉴会计方法讨论的比较多,如国民经济核算的资产负债表的编制,如循环账户中的复式记账法……,无疑使统计核算方法得到了完善。但这也给人们一个错误的信号,以为统计核算方法日益与会计方法靠拢,是否会失去“统计”的特性,实际上这种忧虑大可不必。长期以来,会计方法就借鉴了大量的统计方法,只不过很少有人把会计所借鉴的统计方法系统地总结,使人忽略了统计方法对会计方法的重要支持。本文侧重从统计方法在会计领域的广泛运用谈起,一是说明统计方法自身的重要性和应用性不可低估,二是说明会计和统计虽是两类不同层次的核算体系,但是它们之间通过相互借鉴。加强交流,既不影响它们独自的特性,而且还会促进两个领域的自我完善。     

Features and performance of some outlier detection methods

A review of several statistical methods that are currently in use for outlier identification is presented, and their performances are compared theoretically for typical statistical distributions of experimental data, considering values derived from the distribution of extreme order statistics as reference terms. A simple modification of a popular, broadly used method based upon box-plot is introduced, in order to overcome a major limitation concerning sample size. Examples are presented concerning exploitation of methods considered on two data sets: a historical one concerning evaluation of an astronomical constant performed by a number of leading observatories and a substantial database pertaining to an ongoing investigation on absolute measurement of gravity acceleration, exhibiting peculiar aspects concerning outliers. Some problems related to outlier treatment are examined, and the requirement of both statistical analysis and expert opinion for proper outlier management is underlined.     

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.     

Hidden Second‐order Stationary Spatial Point Processes

In the existing statistical literature, the almost default choice for inference on inhomogeneous point processes is the most well‐known model class for inhomogeneous point processes: reweighted second‐order stationary processes. In particular, the K‐function related to this type of inhomogeneity is presented as the inhomogeneous K‐function. In the present paper, we put a number of inhomogeneous model classes (including the class of reweighted second‐order stationary processes) into the common general framework of hidden second‐order stationary processes, allowing for a transfer of statistical inference procedures for second‐order stationary processes based on summary statistics to each of these model classes for inhomogeneous point processes. In particular, a general method to test the hypothesis that a given point pattern can be ascribed to a specific inhomogeneous model class is developed. Using the new theoretical framework, we reanalyse three inhomogeneous point patterns that have earlier been analysed in the statistical literature and show that the conclusions concerning an appropriate model class must be revised for some of the point patterns.     

互联网统计与广义统计学

论文论述了互联网统计与广义统计学的基本学说和时代要求,提出了以互联网智能化为目标的统计设计及模型开发的全面量化新统计时代的丰富内容,研究了统计工作实践向互联网统计转变、互联网统计和广义统计学对统计工作和统计学科发展的关键作用、互联网统计和广义统计学的理论方法发展,以及政府统计改革的科学性问题和统计挑战人工智能的重要作用等,这些研究对于深刻认识统计实践发展和统计学科建设具有重要的意义。     

Comment on testing for spurious and cointegrated regressions: a wavelet approach

In a recent paper, Leong and Huang [6] proposed a wavelet-correlation-based approach to test for cointegration between two time series. However, correlation and cointegration are two different concepts even when wavelet analysis is used. It is known that statistics based on non-stationary integrated variables have non-standard asymptotic distributions. However, wavelet analysis offsets the integrating order of non-stationary series so that traditional asymptotics on stationary variables suffices to ascertain the statistical properties of wavelet-based statistics. Based on this, this note shows that wavelet correlations cannot be used as a test of cointegration.