Visualizing Mean,Median, Mean Deviation,and Standard Deviation of a Set of Numbers

We review the existing visualizations of the mean and the median of a given set of numbers. Then we give an alternative visualization of the mean using the empirical cumulative distribution function of the given numbers. Next, we visualize the mean deviation (MD) and the mean square deviation (MSD) of the given numbers from any arbitrary value, including the variance. In light of these new visualizations, we revisit the well-known optimal properties of the MD from the median and the MSD from the mean. We also give a more elementary explanation of why the denominator of the sample variance of a set of numbers is one less than the sample size.     

Econometric Applications of the Forward Search in Regression: Robustness,Diagnostics, and Graphics

The article illustrates the use of the forward search to provide robust analyses of econometric data. The emphasis is on informative plots that reveal the inferential importance of each observation. The division of observations into “good” and “bad” leverage points is shown to be potentially misleading.     

作图焦虑量表的开发、验证与应用

当前各行业对信息可视化的需求不断增加,但在未受过可视化专业训练人群中的作图焦虑现象较为普遍。作图者倾向于逃避作图,或对作图软件感到畏惧,而对开发作图焦虑量表进行定量评估则有助于调整教学方式,优化作图软件用户体验。利用探索性因子分析、基于稳健估计结构方程模型和线性回归模型进行分析,结果显示:作图焦虑具有易错性、软件操作、合义性和美观性的四重结构;作图焦虑与电脑效能感、审美效能感等因素之间存在关联。     

The Performance of Panel Cointegration Methods: Results from a Large Scale Simulation Study

This article presents results concerning the performance of both single equation and system panel cointegration tests and estimators. The study considers the tests developed in Pedroni (1999 Pedroni , P. ( 1999 ). Critical values for cointegration tests in heterogeneous panels with multiple regressors . Oxford Bulletin of Economics and Statistics 61 : 653 – 670 .[Crossref], [Web of Science ®] , [Google Scholar], 2004 Pedroni , P. ( 2004 ). Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis . Econometric Theory 20 : 597 – 625 .[Crossref], [Web of Science ®] , [Google Scholar]), Westerlund (2005 Westerlund , J. ( 2005 ). New simple tests for panel cointegration . Econometric Reviews 24 : 297 – 316 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Larsson et al. (2001 Larsson , R. , Lyhagen , J. , Löthgren , M. ( 2001 ). Likelihood-based cointegration tests in heterogeneous panels . Econometrics Journal 4 : 109 – 142 .[Crossref] , [Google Scholar]), and Breitung (2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and the estimators developed in Phillips and Moon (1999 Phillips , P. C. B. , Moon , H. R. ( 1999 ). Linear regression limit theory for nonstationary panel data . Econometrica 67 : 1057 – 1111 .[Crossref], [Web of Science ®] , [Google Scholar]), Pedroni (2000 Pedroni , P. ( 2000 ). Fully modified OLS for heterogeneous cointegrated panels . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 93 – 130 .[Crossref] , [Google Scholar]), Kao and Chiang (2000 Kao , C. , Chiang , M.-H. ( 2000 ). On the estimation and inference of a cointegrated regression in panel data . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 179 – 222 .[Crossref] , [Google Scholar]), Mark and Sul (2003 Mark , N. C. , Sul , D. ( 2003 ). Cointegration vector estimation by panel dynamic OLS and long-run money demand . Oxford Bulletin of Economics and Statistics 65 : 655 – 680 .[Crossref], [Web of Science ®] , [Google Scholar]), Pedroni (2001 Pedroni , P. ( 2001 ). Purchasing power parity tests in cointegrated panels . Review of Economics and Statistics 83 : 1371 – 1375 . [Google Scholar]), and Breitung (2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We study the impact of stable autoregressive roots approaching the unit circle, of I(2) components, of short-run cross-sectional correlation and of cross-unit cointegration on the performance of the tests and estimators. The data are simulated from three-dimensional individual specific VAR systems with cointegrating ranks varying from zero to two for fourteen different panel dimensions. The usual specifications of deterministic components are considered.     

The Performance of Panel Unit Root and Stationarity Tests: Results from a Large Scale Simulation Study

This paper presents results on the size and power of first generation panel unit root and stationarity tests obtained from a large scale simulation study. The tests developed in the following papers are included: Levin et al. (2002), Harris and Tzavalis (1999), Breitung (2000), Im et al. (1997, 2003), Maddala and Wu (1999), Hadri (2000), and Hadri and Larsson (2005). Our simulation set-up is designed to address inter alia the following issues. First, we assess the performance as a function of the time and the cross-section dimensions. Second, we analyze the impact of serial correlation introduced by positive MA roots, known to have detrimental impact on time series unit root tests, on the performance. Third, we investigate the power of the panel unit root tests (and the size of the stationarity tests) for a variety of first order autoregressive coefficients. Fourth, we consider both of the two usual specifications of deterministic variables in the unit root literature.     

产业升级、增长联盟与住房供给弹性——基于35个大中城市的数据分析

产业升级对地方政府与房地产业所形成的增长联盟形成冲击,因此产业变迁对于房地产业的影响已成为理论研究的重点。通过构建住房供给弹性与产业升级、财政收入、政府干预变量的计量模型,运用2009—2015年中国35个大中城市数据,实证分析并检验得出结论:产业升级与财政收入增长会提升住房供给弹性,降低供给调整粘滞效应;而在产业高级化程度与财政收入较低的区域,住房供给调整粘滞效应较大,住房调控政策往往会处于失灵状态。因此,房地产调控长效机制的形成应该建立在产业升级与财政增长的前提之下,并在此基础上提出构建以产业新城为核心的产业地产机制、形成以创新为核心的产业集群效应等政策建议。     

Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

We develop a finite-sample procedure to test the mean-variance efficiency and spanning hypotheses, without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear regression models. The framework allows for unknown forms of nonnormalities as well as time-varying conditional variances and covariances among the model disturbances. We derive exact bounds on the null distribution of joint F statistics to deal with the presence of nuisance parameters, and we show how to implement the resulting generalized nonparametric bounds tests with Monte Carlo resampling techniques. In sharp contrast to the usual tests that are not even computable when the number of test assets is too large, the power of the proposed test procedure potentially increases along both the time and cross-sectional dimensions.     

Detecting Overdispersion in Large Scale Surveys: Application to a Study of Education and Social Class in Britain (with Comments)

A practical problem with large scale survey data is the potential for overdispersion. Overdispersion occurs when the data display more variability than is predicted by the variance–mean relationship for the assumed sampling model. This paper describes a simple strategy for detecting and adjusting for overdispersion in large scale survey data. The method is primarily motivated by data on the relationship between social class and educational attainment obtained from a 2% sample from the 1991 census of the population of Great Britain. Overdispersion can be detected by first grouping the data into a number of strata of approximately equal size. Under the assumption that the observations are independent and there is no variability in the parameter of interest, there is a direct relationship between the nominal standard errors and the empirical or sample standard deviation of the parameter estimates obtained from each of the separate strata. With the 2% sample from the British census data, quite a discernible departure from this relationship was found, indicating overdispersion. After allowing for overdispersion, improved and more realistic measures of precision of the strength of the social class–education associations were obtained.     

Structural breaks in panel data: Large number of panels and short length time series

The detection of (structural) breaks or the so called change point problem has drawn increasing attention from the theoretical, applied economic and financial fields. Much of the existing research concentrates on the detection of change points and asymptotic properties of their estimators in panels when N, the number of panels, as well as T, the number of observations in each panel are large. In this paper we pursue a different approach, i.e., we consider the asymptotic properties when N→∞ while keeping T fixed. This situation is typically related to large (firm-level) data containing financial information about an immense number of firms/stocks across a limited number of years/quarters/months. We propose a general approach for testing for break(s) in this setup. In particular, we obtain the asymptotic behavior of test statistics. We also propose a wild bootstrap procedure that could be used to generate the critical values of the test statistics. The theoretical approach is supplemented by numerous simulations and by an empirical illustration. We demonstrate that the testing procedure works well in the framework of the four factors CAPM model. In particular, we estimate the breaks in the monthly returns of US mutual funds during the period January 2006 to February 2010 which covers the subprime crises.     

Box‐Cox transformations in linear models: Large sample theory and tests of normality

The authors provide a rigorous large sample theory for linear models whose response variable has been subjected to the Box‐Cox transformation. They provide a continuous asymptotic approximation to the distribution of estimators of natural parameters of the model. They show, in particular, that the maximum likelihood estimator of the ratio of slope to residual standard deviation is consistent and relatively stable. The authors further show the importance for inference of normality of the errors and give tests for normality based on the estimated residuals. For non‐normal errors, they give adjustments to the log‐likelihood and to asymptotic standard errors.     

Child health,breast-feeding,and survival in Malaysia: a random-effects logit approach

This study examines the possibility that estimation of the effect of breast-feeding on infant survival is affected by selection bias, in that children who are healthier at birth may be more likely to be breast-fed. Data are from the 1976 Malaysian Family Life Survey. "Ordinary logit models for breast-feeding and survival are estimated, and the results suggest that selection is indeed present. For example, children of higher birth weight appear to be more likely to be breast-fed and likely to survive. In addition, weight at birth and the duration of breast-feeding appear to be linked." Using birth weight as an indicator for the child's health, the authors conclude that "the direct influence of breast-feeding on survival remains of overwhelming importance even after corrections for selection bias are made."     

Bayesian revision of a prior given prior-data conflict,expert opinion,or a similar insight: a large-deviation approach

Learning from model diagnostics that a prior distribution must be replaced by one that conflicts less with the data raises the question of which prior should instead be used for inference and decision. The same problem arises when a decision maker learns that one or more reliable experts express unexpected beliefs. In both cases, coherence of the solution would be guaranteed by applying Bayes's theorem to a distribution of prior distributions that effectively assigns the initial prior distribution a probability arbitrarily close to 1. The new distribution for inference would then be the distribution of priors conditional on the insight that the prior distribution lies in a closed convex set that does not contain the initial prior. A readily available distribution of priors needed for such conditioning is the law of the empirical distribution of sufficiently large number of independent parameter values drawn from the initial prior. According to the Gibbs conditioning principle from the theory of large deviations, the resulting new prior distribution minimizes the entropy relative to the initial prior. While minimizing relative entropy accommodates the necessity of going beyond the initial prior without departing from it any more than the insight demands, the large-deviation derivation also ensures the advantages of Bayesian coherence. This approach is generalized to uncertain insights by allowing the closed convex set of priors to be random.     

Analysis of longitudinal data with drop-out: objectives, assumptions and a proposal

Summary. The problem of analysing longitudinal data that are complicated by possibly informative drop-out has received considerable attention in the statistical literature. Most researchers have concentrated on either methodology or application, but we begin this paper by arguing that more attention could be given to study objectives and to the relevant targets for inference. Next we summarize a variety of approaches that have been suggested for dealing with drop-out. A long-standing concern in this subject area is that all methods require untestable assumptions. We discuss circumstances in which we are willing to make such assumptions and we propose a new and computationally efficient modelling and analysis procedure for these situations. We assume a dynamic linear model for the expected increments of a constructed variable, under which subject-specific random effects follow a martingale process in the absence of drop-out. Informal diagnostic procedures to assess the tenability of the assumption are proposed. The paper is completed by simulations and a comparison of our method and several alternatives in the analysis of data from a trial into the treatment of schizophrenia, in which approximately 50% of recruited subjects dropped out before the final scheduled measurement time.     

The randomized concentration-controlled trial:mathematical definitions,a dose-adjusting algorithm,and sample size efficiency

A randomized concentration-controlled trial (RCCT) (Peck 1990) is distinguished from a randomized dose-controlled trial (RDCT) by controlling the plasma concentration and allowing the dose to vary, as opposed to controlling the dose and allowing the concentration to vary. Monte Carlo studies have suggested that the RCCT is more efficient (in terms of sample size) than the more traditional dose-controlled trials. This paper presents a general mathematical defminition and investigates the properties of an RCCT. A Bayesian adjustment algorithm used in an RCCT is presented and discussed. Expressions for the sample-size efficiency of the RCCT relative to the RDCT is found for both Gaussian and Bernoulli efficacy variables. The RCCT is found to be at least as efficient in terms of sample size. The RCCT can be considerably more efficient than the RDCT.     

Estimating precision,repeatability, and reproducibility from Gaussian and non- Gaussian data: a mixed models approach

Quality control relies heavily on the use of formal assessment metrics. In this paper, for the context of veterinary epidemiology, we review the main proposals, precision, repeatability, reproducibility, and intermediate precision, in agreement with ISO (international Organization for Standardization) practice, generalize these by placing them within the linear mixed model framework, which we then extend to the generalized linear mixed model setting, so that both Gaussian as well as non-Gaussian data can be employed. Similarities and differences are discussed between the classical ANOVA (analysis of variance) approach and the proposed mixed model settings, on the one hand, and between the Gaussian and non-Gaussian cases, on the other hand. The new proposals are applied to five studies in three diseases: Aujeszky's disease, enzootic bovine leucosis (EBL) and bovine brucellosis. The mixed-models proposals are also discussed in the light of their computational requirements.