A Multistage Chi-square Test for Measurement of the Degree of Association in Two-way Table

The classical chi-square test for independence cannot convey additional information and the degree of the association of two factors in two-way contingency table. Besides, measures of association by contingency coefficient need to be used with care, because the association measures depend on the number of rows r and the number of columns c. This article proposes a multistage chi-square test to measure the degree of the association between the two factors in two-way contingency table. We also give simulation and real examples to assess the performance of the proposed method. The results show that our proposed method can effectively investigate the degree of association of two factors in two-way contingency table.     

Major league baseball career length in the 20th century

The sport of baseball has used statistics to enhance understanding for fans for over a century, yet there is limited data on player careers. This study fills that void by examining the careers of baseball players over the last century. Between 1902 and 1993, 5,989 position players started their careers and played 33,272 person years of major league baseball. A rookie position player can expect to play 5.6 years; one in five position players will have only a single-year career, and at every point of a player’s career, the chance of exiting is at least 11%. Position players who start younger and begin their careers in more recent decades all have longer and more stable careers; nevertheless, baseball careers are not compressed versions of normal careers, but are substantially skewed toward early exit.

A comparison of models for dynamic life tables. Application to mortality data from the Valencia Region (Spain)

The graduation of mortality data aims to estimate the probabilities of death at age x, q ( x ), by means of an age-dependent function, whose parameters are adjusted from the crude probabilities that are directly obtainable from the data. However, current life tables have a problem, the need for periodic updates due to changes in mortality over short periods of time. The table containing mortality rates for different ages in different years, q ( xt ), is called a dynamic life table, which captures mortality variation over time. This paper proposes a review of the most commonly used dynamic models and compares the results obtained by each of them when applied to mortality data from the Valencia Region (Spain). The result of the comparison leads us to the conclusion that the Lee-Carter method offers the best results for both sexes, while that based on Heligman and Pollard functions provides the best fit for men alone. Our working method is of additional interest as it may be applied to mortality data for a wide range of ages in any geographical location, allowing the most appropriate dynamic life table to be selected for the case at hand.     

Mass imprisonment and the life course revisited: Cumulative years spent imprisoned and marked for working-age black and white men

Over the last 40 years, imprisonment has become a common stage in the life-course for low-skilled and minority men, with implications not only for inequality among adult men but also for inequality more broadly. Unfortunately, all research documenting how increases in imprisonment have transformed the life-course of poor, minority men has neglected to estimate how much time black and white men on average spend imprisoned or marked as an ex-prisoner. In this article, we fill this gap by using multistate life tables to estimate what share of their working lives (18–64) black and white men will spend imprisoned and marked as ex-prisoners. Our estimates imply that white men spend on average 0.33 years of their working lives imprisoned and 2.31 years marked, while black men spend on average 1.79 years of their working lives imprisoned and 11.14 years marked. This implies that black men spend on average one-third of their working lives either imprisoned or having been freed but marked by the penal system. For the 32.2% of black men who ever experience imprisonment (Bonczar, 2003), moreover, these estimates imply that they spend on average 5.56 years imprisoned, corresponding to 13.4% of their working lives. Taken together, these findings imply a dramatic reorientation of the life course for black men, as one-third of the black male population will spend one-seventh of their working life in prison.     

Generalised quasi‐symmetry models for ordinal contingency tables

This paper extends the ordinary quasi‐symmetry (QS) model for square contingency tables with commensurable classification variables. The proposed generalised QS model is defined in terms of odds ratios that apply to ordinal variables. In particular, we present QS models based on global, cumulative and continuation odds ratios and discuss their properties. Finally, the conditional generalised QS model is introduced for local and global odds ratios. These models are illustrated through the analysis of two data sets.     

Compositional Tables Analysis in Coordinates

Compositional tables – a continuous counterpart to the contingency tables – carry relative information about relationships between row and column factors; thus, for their analysis, only ratios between cells of a table are informative. Consequently, the standard Euclidean geometry should be replaced by the Aitchison geometry on the simplex that enables decomposition of the table into its independent and interactive parts. The aim of the paper is to find interpretable coordinate representation for independent and interaction tables (in sense of balances and odds ratios of cells, respectively), where further statistical processing of compositional tables can be performed. Theoretical results are applied to real‐world problems from a health survey and in macroeconomics.     

Efficient and flexible model-based clustering of jumps in diffusion processes

Jump–diffusion processes involving diffusion processes with discontinuous movements, called jumps, are widely used to model time-series data that commonly exhibit discontinuity in their sample paths. The existing jump–diffusion models have been recently extended to multivariate time-series data. The models are, however, still limited by a single parametric jump-size distribution that is common across different subjects. Such strong parametric assumptions for the shape and structure of a jump-size distribution may be too restrictive and unrealistic for multiple subjects with different characteristics. This paper thus proposes an efficient Bayesian nonparametric method to flexibly model a jump-size distribution while borrowing information across subjects in a clustering procedure using a nested Dirichlet process. For efficient posterior computation, a partially collapsed Gibbs sampler is devised to fit the proposed model. The proposed methodology is illustrated through a simulation study and an application to daily stock price data for companies in the S&P 100 index from June 2007 to June 2017.     

Bayesian analysis of quasi-life tables

Quasi-life tables, in which the data arise from many concurrent, independent, discrete-time renewal processes, were defined by Baxter (1994, Biometrika 81:567–577), who outlined some methods for estimation. The processes are not observed individually; only the total numbers of renewals at each time point are observed. Crowder and Stephens (2003, Lifetime Data Anal 9:345–355) implemented a formal estimating-equation approach that invokes large-sample theory. However, these asymptotic methods fail to yield sensible estimates for smaller samples. In this paper, we implement a Bayesian analysis based on MCMC computation that works equally well for large and small sample sizes. We give three simulated examples, studying the Bayesian results, the impact of changing prior specification, and empirical properties of the Bayesian estimators of the lifetime distribution parameters. We also study the Baxter (1994, Biometrika 81:567–577) data, and uncover structure that has not been commented upon previously.     

Comparison of Four Methods for Estimating Complete Life Tables from Abridged Life Tables Using Mortality Data Supplied to EUROCARE-3

ABSTRACT

To estimate mortality due to cancer, it is necessary to have mortality data by year of age in the population of cancer patients. When such data are not available, estimating one-year (complete) life tables from five-year (abridged) life tables is necessary. Four such methods—Elandt–Johnson, Kostaki, Brass logit, and Akima spline methods—are compared with respect to 782 empirical complete life tables pertaining to 19 European regions or countries, from 1954 to 2000. Abridged life tables are first derived from the empirical ones, then used to produce one-year-life tables by each of the four methods. These reconstituted complete life tables are then compared with the empirical complete life tables. Among the four methods, the Elandt–Johnson demographic method produces the best reconstitutions at adult ages, specifically those ages at which observed cancer survival needs to be corrected.     

Applications of sequential set partitioning: a set of technical information systems problems

Many problems that appear in different contexts are conceptually similar and so are amenable to solution by a common technique. Three such technical Information Systems (IS) problems are: (1) segmentation of computer programs; (2) attribute discretization for decision tree induction; and (3) design of hash tables in database systems. In this paper we show how each of these seemingly different problems can be formulated as a sequential (set) partitioning problem, and solved using a parametric linear programming (LP) procedure. This approach provides optimal solutions unlike previous solution approaches which were either greedy heuristics or limited to solving only a specific problem situation. Given the likelihood that other applications of the sequential partitioning problem exist in IS, the material presented here could be useful to other researchers in formulating the problem at an appropriate level of abstraction so that available optimal solution approaches can be identified. In addition to providing a common solution method, parametric LP frees the user from having to make premature decisions regarding the number of groups for the partition, and this decision can be delayed post solution.