A Symposium on Unemployment Statistics

Separate Poisson distributions were evaluated via several hypotheses tests for each of the 16 teams in the National Hockey League using 1973–74 goals for and goals against both home and away. After examining independence of goals for and goals against, they in turn were used to explain order of finish for the 16 teams. The results were quite surprising.     

Robust Two-Sample Statistics for Testing Equality of Means: a Simulation Study

When testing the equality of the means from two independent normally distributed populations given that the variances of the two populations are unknown but assumed equal, the classical two-sample t-test is recommended. If the underlying population distributions are normal with unequal and unknown variances, either Welch's t-statistic or Satterthwaite's Approximate F-test is suggested. However, Welch's procedure is non-robust under most non-normal distributions. There is a variable tolerance level around the strict assumptions of data independence, homogeneity of variances and normality of the distributions. Few textbooks offer alternatives when one or more of the underlying assumptions are not defensible.     

Diagnostic tests as residual analysis

Many applied workers are strongly oriented to residual analysis for assessing model adequacy. Formal test statistics of adequacy however are frequently derived from likelihood theory, particularly through Lagrange Multipliers. In contraGt, the present paper derives the formal statistics by concentrating Upon the distribution of residuals. It is shown that most existing tests can be derived in this way from a few elementary principles of specification analysis. One advantage of this alternative methodology is that it highlights some difficulties in existing approaches and simultaneously indicates a resolution of them; a good example being testing for heteroscedasticity in simultaneous equations. Other issues such as independence and robustness of diagnostic tests are also easily explored within the proposed framework.     

Nuisance Parameters and the Use of Exploratory Graphical Methods in a Bayesian Analysis

Consider the problem of inference about a parameter θ in the presence of a nuisance parameter v. In a Bayesian framework, a number of posterior distributions may be of interest, including the joint posterior of (θ, ν), the marginal posterior of θ, and the posterior of θ conditional on different values of ν. The interpretation of these various posteriors is greatly simplified if a transformation (θ, h(θ, ν)) can be found so that θ and h(θ, v) are approximately independent. In this article, we consider a graphical method for finding this independence transformation, motivated by techniques from exploratory data analysis. Some simple examples of the use of this method are given and some of the implications of this approximate independence in a Bayesian analysis are discussed.     

人口城市化与产业结构变迁——基于湖南省的实证检验

本文从城市化与产业结构优化的关系出发运用基于VAR模型的动态计量经济方法对湖南省人口城市化对产业结构优化的作用进行了实证研究。实证结果表明城市化对于产业结构具有长期效应。产值结构上表现为城市化对第一产业具有持久的负向影响,但对第二产业具有长期稳定的正向影响,对第三产业的影响具有时滞性：就业结构上表现为对第一产业有着长期的负向效应,对第三产业具有持久的正向效应,但与第二产业长期关系不显著。整体来看,城市化在促进湖南经济的发展、推动产业结构优化升级中发挥着重要的作用。由此提出相关的政策建议。     

Invariant tests for multivariate normality: a critical review

d -dimensional random vector X is some nondegenerate d-variate normal distribution, on the basis of i.i.d. copies X ₁, ..., X _x of X. Particular emphasis is given to progress that has been achieved during the last decade. Furthermore, we stress the typical diagnostic pitfall connected with purportedly ‘directed’ procedures, such as tests based on measures of multivariate skewness. Received: April 30, 2001; revised version: October 30, 2001     

Cointegration and direct tests of the rational expectations hypothesis

The paper is concerned with direct tests of the rational expectations hypothesis (REH) in the presence of stationary and non-stationary variables. Alternative methods of converting qualitative survey responses into quantitative expectations series are examined. Testing of orthogonality and the issue of generated regressors for models estimated by two step methods are re-evaluated when the variable to be explained is stationary. A methodological approach for testing the REH is provided for models using qualitative response data when there are unit roots and cointegration, and alternative reasons are examined for rejecting the null hypothesis of orthogonality. The usefulness of cointegration analysis for both the probability and regression conversion procedures is also analysed. Cointegration is found to be directly applicable for the probability conversion approach with uniform, normal and logistic distributions of expectations and for the linear regressicn conversion approach. In the light of new techniques, an existing empirical example testing the REH for British manufacturing firms is re-examined and tested over an extended data set.     

A monte carlo analysis of two spectral tests of the martingale hypothesis

Summary The size, power, and robustness properties of the Kolmogorov-Smirnov and Cramér-von Mises spectral tests of the martingale (difference) hypothesis are investigated by Monte Carlo methods. The results highlight a marked superiority of the Cramér-von Mises with respect to the Kolmogorov-Smirnov test. The paper also shows that the Cramér-von Mises test is simple to compute, more general and more powerful than other converntionally used tests.     

Comparing a new Gini test with other symmetry tests when median is known

ABSTRACT

Wang et al. (2013 Wang, J. C., H. Auda, and M. Niewiadomska-Bugaj. 2013. Comparing a new Gini test with other symmetry tests when median is unknown. Communications in Statistics- Simulation and Computation 42:1616–27.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) provided a comprehensive study of 14 tests, including two tests based on the Gini mean difference (GMD) introduced by Auda (2006), applicable for data from populations with an unknown median. This paper is a similar study of symmetry tests applicable for data from populations with a known median. We are showing that GMD tests compare favorably with several existing procedures in controlling the type I error as well as in power. Results of the study are shown graphically, which makes the tests’ power easy to assess.     

Rejoinder

Abstract

In this article several formulae for the approximation of the critical values for tests on the actual values of the process capability indices CPL, CPU, and C_pk are provided. These formulae are based on different approximations of the percentiles of the noncentral t distribution and their performance is evaluated by comparing the values assessed through them from the exact critical values, for several significance levels, test values, and sample sizes. As supported by the obtained results, some of the presented techniques constitute valuable tools in situations where the exact critical values of the tests are not available, since one may approximate them readily and rather accurately through them.