ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.     

Contingency tables with structural zeros

In this paper, the method of Hocking and Oxspring (1971) to estimate multinomial probabilities when full and partial data are available for some cells is extended to estimate the cell probabilities of a contingency table with structural zeros. The estimates are maximum likelihood, and the process is sequential. The gain in precision is due to the use of partial data and the bias of the estimates is also investigated.     

In Memoriam: Frank Wilcoxon

A mosaic is a graphical display of cross-classified data in which each count is represented by a rectangle of area proportional to the count. The positions and sides of the rectangles are set to encourage comparisons between counts in the figures. Mosaics are useful for discovering unusually high or small counts and for discovering dependencies between variables. In principle, mosaics may be used for any number of cross-classifying variables, but six seems to be a practical maximum. A mosaic is given for a four-way classification of Nielsen ratings.     

Quantitative refinements for comparisons of institutional performance

In the context of the data and issues discussed by Goldstein and Spiegelhalter, we suggest refinements which can be used by decision makers when confronted with ranking problems associated with 'league tables'. Two ranking criteria are defined and their performance illustrated for one of the studies reported by Goldstein and Spiegelhalter.     

Exact and resampling probability values for the Piccarreta nominal–ordinal index of association

Exact, resampling, and Pearson type III permutation methods are provided to compute probability values for Piccarreta's nominal–ordinal index of association. The resampling permutation method provides good approximate probability values based on the proportion of resampled test statistic values equal to or greater than the observed test statistic value.     

传递图表信息：《经济学》双语教学的重要环节

引进外文原版教材、使用英语等外语对公共课和专业课进行双语教学是我国高等教育与国际接轨的重要途径。文章归纳总结了《经济学》所采用的分析工具——图表的种类及其特征,分析了图表之间相互转换所应注意的问题及其对于英语写作的启发意义,进而论证了双语教学的语言提升功能。     

Resolving the conflict over fisher's exact test

Fisher's exact test for two-by-two contingency tables has repeatedly been criticized as being too conservative. These criticisms arise most frequently in the context of a planned experiment for which the numbers of successes in each of two experimental groups are assumed to be binomially distributed. It is argued here that the binomial model is often unrealistic, and that the departures from the binomial assumptions reduce the conservatism in Fisher's exact test. Further discussion supports a recent claim of Barnard (1989) that the residual conservatism is attributable, not to any additional information used by the competing method, but to the discrete nature of the test, and can be drastically reduced through the use of Lancaster's mid-p-value. The binomial model is not recommended in that it depends on extra, questionable assumptions.     

A New Look at an Old Test

Fisher's exact test for 2 × 2 frequency tables is presented in a new format which, we believe, is easier to use and which permits a substantial saving in tabulation-space of critical values. Tables are provided here for total frequency N ≤ 25. Tables for N ≤ 100 are obtainable on request to the author     

Policy responses to COVID-19 pandemic waves: Cross-region and cross-sector economic impact

This paper proposes a modelling approach to assess the cross-region and cross-sector economic impacts of the restrictions imposed by governments to contain the COVID-19 pandemic. The nationwide lockdown imposed in Italy during the first wave of the pandemic is used as a benchmark. However, the adopted approach allows an ex-ante assessment of alternative policy responses, in the event of successive pandemic waves, in order to rationalise the policy intervention and reach the best possible compromise between containing the risk of contagion and reducing economic losses. The used approach consists of a non-linear programming model based on a multiregional Input-Output (I-O) table, which guarantees greater flexibility than traditional I-O analysis. It is applied to estimate both direct and indirect losses of GDP and employment produced by alternative policy responses represented by general and differentiated lockdowns. The evidence deriving from the Italian experience shows a sort of learning process through successive waves based on the introduction of increasingly flexible and tailored policy responses to the pandemic.     

KENDALL'S TAU AND CONTINGENCY TABLES

Kendall's tau is a coefficient of concordance between two rankings of n objects. Its definition and large sample normal approximation are easily extended to the case where one of the rankings contains ties. In this paper, definition and normal approximation are extended further to the case where both rankings contain ties. The results are applied to give a fully distribution-free test for two-way contingency tables with ordered categories.