The importance of being earnest in statistics

The principal assumption of statistical theory is that a sample came from a homogeneous population. This assumption is not tested when statistical computations are produced. It creates a gap between statistical theory and statistical practice. This gap is bridged by the new quality philosophy (NQP) in statistics. The NQP defines a homogeneous population in terms of classical probability discrete distributions.     

独立学院《概率论与数理统计》教学改革探讨

独立学院作为我国高等教育大众化的产物,是一种新的办学模式。开拓独具特色的"应用型人才培养"模式是三本院校持续发展的保障。而概率论与数理统计作为应用性广泛的数学分支是一门重要的基础课程,那么对当前三本院校的概率论与数理统计如何改革,才能既符合独立学院的办学模式。探索一些改革措施,对提高教学质量具有重要的意义。文章从教学方法,教学内容,教学结构以及教材选取等多方面探讨了独立学院概率论与数理统计的改革。     

假设检验的启发式教学方法研究

假设检验是概率论与数理统计课程教学中的重点和难点。针对以往教学中出现的弊端,本文通过启发式教学方法,使学生在掌握原理的同时树立主动思维与统计思想。     

Testing the adequacy of varying coefficient models with missing responses at random

In this paper, we investigate checking the adequacy of varying coefficient models with response missing at random. In doing so, we first construct two completed data sets based on imputation and marginal inverse probability weighted methods, respectively. The empirical process-based tests by using these two completed data sets are suggested and the asymptotic properties of the test statistics under the null and local alternative hypotheses are studied. Because the limiting null distribution is intractable, a Monte Carlo approach is applied to approximate the distribution to determine critical values. Simulation studies are carried out to examine the performance of our method, and a real data set from an environmental study is analyzed for illustration.     

An information fusion FMEA method to assess the risk of healthcare waste

Healthcare waste (HCW) management plays a vital role in the development of modern society. In HCW management, failure mode and effects analysis (FMEA) is a popular method to implement risk management for improving the quality of healthcare. However, the shortcomings of the traditional FMEA method have been widely discussed in literatures. This paper proposes an information fusion FMEA method based on 2-tuple linguistic information and interval probability. The 2-tuple linguistic set theory is adopted to change the heterogeneous information into interval numbers. Meanwhile, the interval probability comparison method is applied to analyze failure modes. Finally, a case study is presented to verify the reliability and effectiveness of the proposed method by comparing different FMEA methods.     

The homogeneity problem in statistics

The theory of probability is the most abstract mathematical science with unlimited scope of application. However, the essential question of the theory of probability has not been solved: how can we use probabilities in the epistemology of empirical data sets? The answer to this question can be given on the basis of the concept of homogeneous random processes.     

Excel在岩土勘察指标统计中的应用

为了克服在利用专业勘察软件进行岩土物理力学性质指标进行分层统计时,要让有的数据不参加统计计算时操作不便、统计结果不能立即显示,统计结果如不合适又得重头再来一遍的缺点,将专业勘察软件生成的分层数据导入Excel中,采用Excel方法进行各种指标分层统计计算,形成Excel模板后可多次重复使用,经实际使用,计算过程透明、结果同步显示、数据准确,可在工作中应用。     

Random Recursive Partitioning: a matching method for the estimation of the average treatment effect

In this paper we introduce the Random Recursive Partitioning (RRP) matching method. RRP generates a proximity matrix which might be useful in econometric applications like average treatment effect estimation. RRP is a Monte Carlo method that randomly generates non‐empty recursive partitions of the data and evaluates the proximity between two observations as the empirical frequency they fall in a same cell of these random partitions over all Monte Carlo replications. From the proximity matrix it is possible to derive both graphical and analytical tools to evaluate the extent of the common support between data sets. The RRP method is “honest” in that it does not match observations “at any cost”: if data sets are separated, the method clearly states it. The match obtained with RRP is invariant under monotonic transformation of the data. Average treatment effect estimators derived from the proximity matrix seem to be competitive compared to more commonly used estimators. RRP method does not require a particular structure of the data and for this reason it can be applied when distances like Mahalanobis or Euclidean are not suitable, in the presence of missing data or when the estimated propensity score is too sensitive to model specifications. Copyright © 2008 John Wiley & Sons, Ltd.     

Information Measures in Perspective

Information-theoretic methodologies are increasingly being used in various disciplines. Frequently an information measure is adapted for a problem, yet the perspective of information as the unifying notion is overlooked. We set forth this perspective through presenting information-theoretic methodologies for a set of problems in probability and statistics. Our focal measures are Shannon entropy and Kullback–Leibler information. The background topics for these measures include notions of uncertainty and information, their axiomatic foundation, interpretations, properties, and generalizations. Topics with broad methodological applications include discrepancy between distributions, derivation of probability models, dependence between variables, and Bayesian analysis. More specific methodological topics include model selection, limiting distributions, optimal prior distribution and design of experiment, modeling duration variables, order statistics, data disclosure, and relative importance of predictors. Illustrations range from very basic to highly technical ones that draw attention to subtle points.     

数学建模在独立学院的概率统计教学改革中的应用

文章提出了将数学建模思想融入概率统计的教学过程中,并引入案例教学法,以实现理论与实际的无缝连接,从而为引起学生学习数学的积极性,实现将独立学院的学生培养成应用型创新型人才的目标做铺垫。     

Macro‐integration with inequality constraints: an application to the integration of transport and trade statistics

Macro‐integration is the process of combining data from several sources at an aggregate level. We review a Bayesian approach to macro‐integration with special emphasis on the inclusion of inequality constraints. In particular, an approximate method of dealing with inequality constraints within the linear macro‐integration framework is proposed. This method is based on a normal approximation to the truncated multivariate normal distribution. The framework is then applied to the integration of international trade statistics and transport statistics. By combining these data sources, transit flows can be derived as differences between specific transport and trade flows. Two methods of imposing the inequality restrictions that transit flows must be non‐negative are compared. Moreover, the figures are improved by imposing the equality constraints that aggregates of incoming and outgoing transit flows must be equal.     

Über ein nichtparametrisches Schätzproblem

Summary This note gives invariantly optimal estimators for functions of probability densities, based on independent observations in a homogeneous space. The results are applied to the estimation of certain densities, derivatives of the density, densities of order statistics and of empirical means.

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Herrn Professor Dr.Leopold Schmetterer zum 60. Geburtstag gewidmet.     

客观现象的概率统计解释举例

本文通过应用概率统计方法解释人类行为与认识活动实例的分析,说明了基于概率统计方法如何描述客观现象和理解人类的认识行为,进而得出概率统计方法是基于归纳的演绎推理,其本质是认识论中的归纳推理。     

Attempt to test impact values for multi-indicator systems—exemplified by gender equality

Hasse diagram technique, based on partial ordering is an advantageous method to analyse complex systems of data such as objects characterized by multi-indicator systems. Beside ordered sequences of objects the theory may reveal the impact of each indicator for the set of order relations, which in general is of high interest. A method to measure the impact has already been known for more than 20 years; however, up to now there is no method for a testing as to how far these impacts are considered to be relevant. The actual study presents a first attempt for a testing theory, albeit an extension to statistical testing framework is still open. The testing approach so far is applied to the indicators of gender-equality. It turns out that for the 28 nations (pre-Brexit) of the EU, 2006, in addition to the unified European Union only one indicator can definitely be declared as relevant.

     

The influence of cause marketing associations on product and cause brand value

• The purpose of the study presented in this paper is to add to our understanding of the added value, both monetary and non‐monetary, to a brand when supporting a cause in a cause marketing ad. The findings show that consumers do not perceive the brand to be worth more if it was shown to be supporting a cause. The study also failed to show a significant improvement in consumer brand attitudes for brands featured in cause marketing ads. However, there was an attitude improvement for the cause. Product type and consumer dispositional variables were also examined.
• In summary, this study calls into question the value brands derive from being paired with a cause. This study discusses productive areas of future research and managerial implications.

Copyright © 2008 John Wiley & Sons, Ltd.     

Using crowdsourced data to analyze transport crime

ABSTRACT

Anecdotal evidence suggests that harsh social conditions in the road haulage industry are having an impact on transport crime. This paper analyses transport crime, and demonstrates how to use a combination of official statistics and crowdsourced data in the process. A hierarchical regression analysis was applied to investigate the relations among different factors in order to predict transport crime threats. A secondary data set on transport crime from the Swedish Police was combined with primary crowdsourced data from volunteer observations of trucks in Sweden from both high-wage and low-wage countries. The findings imply that transportation is more vulnerable to antagonistic threats in geographical areas where the low-wage hauliers operate more frequently. For policymakers and practitioners, these findings provide useful guidance for the planning of security measures. To the authors’ knowledge, this paper is the first exploratory study of its kind that uses a combination of official statistics and crowdsourced data.     

AN ALGORITHMIC INFORMATION THEORETIC APPROACH TO THE BEHAVIOUR OF FINANCIAL MARKETS

Using frequency distributions of daily closing price time series of several financial market indices, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information theory, may account for some of the deviation of financial markets from log‐normal, and if so for how much of said deviation and over what sequence lengths. We do so by comparing the distributions of binary sequences from actual time series of financial markets and series built up from purely algorithmic means. Our discussion is a starting point for a further investigation of the market as a rule‐based system with an algorithmic component, despite its apparent randomness, and the use of the theory of algorithmic probability with new tools that can be applied to the study of the market price phenomenon. The main discussion is cast in terms of assumptions common to areas of economics in agreement with an algorithmic view of the market.     

What is the effect of university education on chances to be self-employed in transitional countries?: Instrumental variable analysis of cross-sectional sample of 29 nations

We used a high-quality cross-sectional data set that covers a diverse set of 29 transitional countries, to find the effect of education of probability of people being self-employed using standard probit models and instrumental variable biprobit that address endogeneity. Our findings suggest a negative effect of university education on the propensity of being self-employed. This finding remains the same for the single-stage model (i.e. standard probit) and the instrumental variable model (i.e. biprobit). We found strong endogeneity in the estimation of education effect on the propensity of being self-employed, ignoring which renders estimations biased. Regression models, which do not address endogeneity tend to underestimate the negative effect of the education on the probability of being self-employed in the countries of transition. Researchers should use alternative approaches to reduce endogeneity, such as instrumental variables and longitudinal analysis.     

Computer algebra in probability and statistics

This paper discusses the uses of computer algebra within statistics and probability. A distinction is drawn between the use of computer algebra packages to support investigations, by performing calculations, ankl their use to implement structure; to build in elements of a theory (such as stochastic calculus or the Taylor string theory of Barndorff Nielsen and others) as a preliminary to research investigations. Brief surveys are given of instances in the literature of use of computer algebra in probability and statistics. Two examples of implementations of structure are discussed, both drawn from the author's own work with the computer algebra package REDUCE. One is a simple demonstration using moments of the Poisson distribution. The other is itovsn3 , an implementation of the semimartingale stochastic calculus. It is described how itovsn3 may be used to derive the characteristic function of the Lévy stochastic area, following a proof due to S. Janson. Prospects for future work and for work in progress are discussed.