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.     

Regression Revisited

Sir Francis Galton introduced median regression and the use of the quantile function to describe distributions. Very early on the tradition moved to mean regression and the universal use of the Normal distribution, either as the natural ‘error’ distribution or as one forced by transformation. Though the introduction of ‘quantile regression’ refocused attention on the shape of the variability about the line, it uses nonparametric approaches and so ignores the actual distribution of the ‘error’ term. This paper seeks to show how Galton's approach enables the complete regression model, deterministic and stochastic elements, to be modelled, fitted and investigated. The emphasis is on the range of models that can be used for the stochastic element. It is noted that as the deterministic terms can be built up from components, so to, using quantile functions, can the stochastic element. The model may thus be treated in both modelling and fitting as a unity. Some evidence is presented to justify the use of a much wider range of distributional models than is usually considered and to emphasize their flexibility in extending regression models.     

Macroeconomic forecasting using penalized regression methods

We study the suitability of applying lasso-type penalized regression techniques to macroe-conomic forecasting with high-dimensional datasets. We consider the performances of lasso-type methods when the true DGP is a factor model, contradicting the sparsity assumptionthat underlies penalized regression methods. We also investigate how the methods handle unit roots and cointegration in the data. In an extensive simulation study we find that penalized regression methods are more robust to mis-specification than factor models, even if the underlying DGP possesses a factor structure. Furthermore, the penalized regression methods can be demonstrated to deliver forecast improvements over traditional approaches when applied to non-stationary data that contain cointegrated variables, despite a deterioration in their selective capabilities. Finally, we also consider an empirical applicationto a large macroeconomic U.S. dataset and demonstrate the competitive performance of penalized regression methods.     

Term structure estimation in the presence of autocorrelation

This paper assesses the effects of autocorrelation on parameter estimates of affine term structure models (ATSM) when principal components analysis is used to extract factors. In contrast to recent studies, we design and run a Monte Carlo experiment that relies on the construction of a simulation design that is consistent with the data, rather than theory or observation, and find that parameter estimation from ATSM is precise in the presence of serial correlation in the measurement error term. Our findings show that parameter estimation of ATSM with principal component based factors is robust to autocorrelation misspecification.     

企业社会责任报告语调与分析师预测：信号还是迎合？

运用文本分析方法提取了2010—2018年上市公司社会责任报告的文本语调信息，基于信号理论和迎合理论探讨企业社会责任报告语调对分析师预测的影响。研究发现，企业社会责任报告的净正面语调降低了分析师预测偏差和分析师预测分歧度，并且在分析师预测存在乐观偏差时这种作用更加显著。进一步分析发现，企业社会责任报告语调对分析师预测的积极作用仅发生在强制披露和不遵守可持续发展报告指南的企业中以及经验较少、非明星分析师中。经济后果检验发现，社会责任报告语调通过降低分析师预测偏差和分歧度缓解了公司股价崩盘风险。研究结论不仅有助于丰富非财务信息披露经济后果和分析师预测影响因素两个领域的学术文献，而且可以为监管部门合理规范企业社会责任报告披露和投资者有效利用企业社会责任报告中的语调信息提供有益借鉴。     

Influence of research design upon data analysis

Considerations regarding the interrelationships among theory, research design, observational approaches, and data analysis techniques bear on the consistency and integration of our overall procedures in performing social research. It is here illustrated how an initial research conclusion, shown through further analysis to be false, might have been avoided entirely if a more stringent research design had been employed. In a medical treatment context a worrisome negative correlation between treatment and outcome is revealed as spurious, due to gender differences in reactions to a serious disease. If subjects had been randomly assigned to experimental and control groups, a zero correlation coefficient would have correctly indicated that the treatment had no effect upon the outcome.     

Which statistical technique should i use? a survey and marketing case study

Mini and microcomputers are putting an even larger number of powerful statistical analysis techniques at the disposal of the researcher. This paper uses a case study approach to show how to use the original objectives and purpose of a research project to design the study, organize the data collection and select the most appropriate multi-variate technique. Multiple regression, correlation analysis, principal component and factor analysis, discriminant analysis, causal link analysis, cluster analysis, analysis of variance including automatic interaction detection, and canonical correlation analysis are among the models and statistical techniques described in terms of their requirements, underlying hypotheses, limits, advantages. The use of these techniques is illustrated by the study of the “enjoyment” of the tourists who visited the province of Quebec in 1975.     

Ensuring creative approaches in information system design

Improvement in computing capability is one way to aid US companies in recapturing competitive edge. The easy applications have been computerized; the difficult ones lie ahead. Creative approaches are needed to computerize those difficult applications. Yet IS has apparently little interest in the subject of creativity; less than a half-dozen articles on the subject have been published in the 35-year history of the discipline. The author reviewed the literature in other disciplines of art, science, engineering, psychology and education, to determine how creativity techniques had been utilized in those disciplines. The research revealed that many of those techniques are useful for the IS field. Definitions of creativity are provided, then three classifications of creativity research are reviewed: Rothenberg, Ackoff/Vergara, and Rosner/Abt. Creativity techniques are illustrated for general problem solving. The author advocates the use of creativity techniques in the information system development process at four points: near the conclusion of requirements definition, logical design, physical design and program design. Use of creativity techniques at each of these points is illustrated. By delaying convergence on a solution, new approaches and new alternatives can be generated and evaluated. These approaches can produce the systems needed to assist US companies in international competition.     

Microeconomic foundations of corporate strategy

This paper examines several approaches to corporate strategic planning in the context of their relationship to the microeconomic theory of the firm, and discusses the implications of that theory for corporate strategy in general. Specifically, three types of analytical tools are discussed: (1) analytical portfolio models; (2) business simulation models; and (3) optimization models. Examples of how the three types of tools are used in corporate decision-making are given, and certain limitations are cited. The limitations include, for example, the inability of some of the models to deal with interdependencies across business units in production resources or output demand. Finally, the paper examines the approach to strategic planning known as the ‘strategy matrix’, which explicitly allows for interdependices across business units. The use of the strategy matrix by a major petroleum company is discussed in some detail.     

Distinguishing external from internal scale effects: The case of public infrastructure

The recent applied production theory literature focusing on the economic performance of firms has increasingly recognized the importance of scale effects on costs and therefore efficiency. These scale effects may include short run returns due to fixity of privately demanded inputs (i.e., capital, long run internal returns to scale, and external factors affecting costs. Since these different types of scale effects can be thought of as shifts in and movements along cost curves, the different cost effects of such factors can be identified in a framework which explicitly takes them into account in the definition ofscale.In this article we formalize such a framework, and then use it to measure short run, long run (internal) and external scale effects from fixity of private capital, nonconstant returns to scale and public infrastructure. We then use these measures to identify the impacts of these different scale factors on productivity growth. The focus on public infrastructure as an important external scale factor is motivated by the current theoretical and policy interest in this issue; we show how a structural production theory model provides a rich basis for the analysis of the cost effects of infrastructure investment.     

Selecting Adaptive Survey Design Strata with Partial R‐indicators

Recent survey literature shows an increasing interest in survey designs that adapt data collection to characteristics of the survey target population. Given a specified quality objective function, the designs attempt to find an optimal balance between quality and costs. Finding the optimal balance may not be straightforward as corresponding optimisation problems are often highly non‐linear and non‐convex. In this paper, we discuss how to choose strata in such designs and how to allocate these strata in a sequential design with two phases. We use partial R‐indicators to build profiles of the data units where more or less attention is required in the data collection. In allocating cases, we look at two extremes: surveys that are run only once, or infrequent, and surveys that are run continuously. We demonstrate the impact of the sample size in a simulation study and provide an application to a real survey, the Dutch Crime Victimisation Survey.     

Comparison of solutions to the multi-country Real Business Cycle model

We compare the performance of perturbation, projection, and stochastic simulation algorithms for solving the multi-country RBC model described in Den Haan et al. (this issue). The main challenge of solving this model comes from its large number of continuous-valued state variables, ranging between four and 20 in the specifications we consider. The algorithms differ substantially in terms of speed and accuracy, and a clear trade-off exists between the two. Perturbation methods are very fast but invoke large approximation errors except at points close to the steady state; the projection methods considered are accurate on a large area of the state space but are very slow for specifications with many state variables; stochastic simulation methods have lower accuracy than projection methods, but their computational cost increases only moderately with the state-space dimension. Simulated series generated by different methods can differ noticeably, but only small differences are found in unconditional moments of simulated variables. On the basis of our comparison, we identify the factors that account for differences in accuracy and speed across methods, and we suggest directions for further improvement of some approaches.     

战时导弹保障路径的随机规划优化模型

针对战时导弹保障路径规划这一组合优化问题,在分析导弹保障路径优化过程中的不确定性因素的基础上,以时间、可靠度、损耗为置信度,运用网络图及不确定机会约束理论构建了导弹保障路径优化的随机规划模型,并通过具体案例来模拟验证模型的合理性和有效性。     

A critical evaluation of alternative methods and paradigms for conducting mediation analysis in operations management research

Mediation as a theory testing approach has witnessed considerable adoption among Operations Management (OM) researchers. Although mediation-testing methods have evolved tremendously in the past decade, their dissemination in the OM field has not seen parallel growth. These advanced techniques facilitate the testing of existing and complex hypotheses in a more precise manner. With the intent of critically evaluating existing and alternative methods for conducting mediation analysis needed to support sophisticated empirical research, this paper first reviews OM studies that tested for mediation in the past eleven years (2002–2012) from top-tier OM journals. Four commonly used mediation approaches were identified. Based on principles of good theory building, type of mediation model, and properties of empirical data, we evaluate the existing methodologies and make recommendations on how to improve the rigor of OM mediation testing. Using published OM studies in top journals as examples, we then illustrate the relevance and advantages of these recommendations, as well as their ease of use. Furthermore, we empirically show that more robust and insightful results can be achieved by adopting these techniques, which in turn have the promise of leading to better theory building and testing in the field of operations management.     

Simulation Evidence on Theory‐based and Statistical Identification under Volatility Breaks

Beside a priori theoretical assumptions on instantaneous or long‐run effects of structural shocks, sign restrictions have become a prominent means for structural vector autoregressive (SVAR) analysis. Moreover, changes in second order moments of systems of time series can be fruitfully exploited for identification purposes in SVARs. By means of Monte Carlo studies, we examine to what degree theory‐based and statistical identification approaches offer an accurate quantification of the true structural relations in a standard model for monetary policy analysis. Subsequently, we discuss how identifying information from theory‐based and statistical approaches can be combined on the basis of a low‐dimensional empirical model of US monetary policy.     

Pricing in a Service Sector Context: Accounting and Marketing Logics in the Hotel Industry

The paper analyses hotel room pricing via an application of institutional economic theory. The institutional framework considers the impact of accounting and marketing templates that help hotel managers make sense of complex pricing decisions. From an institutional perspective, the spread and implementation of these templates is influenced by specific historical factors and may be subject to path dependency. The institutional theory is applied to a case study using a pragmatic constructivist methodology. The case site revealed that whilst long run cost structures are important in locating the market niche of the business and that hotels use conventional cost control techniques, costs play relatively little role in price determination with a dominant role for marketing templates that concentrate on revenue management. The study suggests how the synthesis between institutional economics and pragmatic constructivism offers a research framework that could be replicated in further studies.     

Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?

Principal component analysis (PCA) is a method of choice for dimension reduction. In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to perform the PCA of streaming data and/or massive data. Despite the wide availability of recursive algorithms that can efficiently update the PCA when new data are observed, the literature offers little guidance on how to select a suitable algorithm for a given application. This paper reviews the main approaches to online PCA, namely, perturbation techniques, incremental methods and stochastic optimisation, and compares the most widely employed techniques in terms statistical accuracy, computation time and memory requirements using artificial and real data. Extensions of online PCA to missing data and to functional data are detailed. All studied algorithms are available in the  package onlinePCA on CRAN.     

Regime shifts in stock–flow I(2)–I(1) systems: the case of US fiscal sustainability

In the last two decades, fiscal sustainability has been tested through the use of non‐stationary time series analysis. Two different approximations can be found in the literature: first, a univariate approach that has focused on the stochastic properties of the stock of debt and, second, a multivariate one that has focused on the long‐run properties of the flows of expenditures and revenues, i.e., in the stochastic properties of the deficit. In this paper we unify these approaches considering the stock–flow system that fiscal variables configure. Our approach involves working in an I(2) stochastic processes framework. Given the possibility of the existence of regime shifts in the sustainability of US deficit that the literature has pointed out, we develop a new statistic that can be applied to test several types of I(2) cointegration and multicointegration relationships allowing for regime shifts. To test for these kinds of changing long‐run relationships we propose the use of a residual‐based Dickey–Fuller class of statistic that accounts for one structural break. We show that consistent estimates of the break fraction can be obtained through the minimization of the sum of squared residuals when there is I(2) cointegration. The finite sample performance of the proposed statistic is investigated by Monte Carlo simulations. The econometric methodology is applied to assess whether the US fiscal deficit and debt are sustainable. Copyright © 2010 John Wiley & Sons, Ltd.