Yule–Simpson’s paradox: the probabilistic versus the empirical conundrum

Statistical Methods & Applications - The current literature views Simpson’s paradox as a probabilistic conundrum by taking the premises (probabilities/parameters/ frequencies) as known....     

Bootstrapping mean‐squared errors of robust small‐area estimators: Application to the method‐of‐payments surveys data

This paper proposes a new bootstrap procedure for mean‐squared errors of robust small‐area estimators. We formally prove the asymptotic validity of the proposed bootstrap method and examine its finite‐sample performance through Monte Carlo simulations. The results show that our procedure performs well and competes with existing ones. We also provide an application to the estimation of the total volume and value of cash, debit card, and credit card transactions in Canada as well as in its provinces and subgroups of households. In particular, we found that there is a significant average annual decline rate of 3.1% in the volume of cash transactions and that this decline is relatively higher among high‐income households living in heavily populated provinces. Our bootstrap estimator also provides indicators of quality useful in selecting the best small‐area predictor among several alternatives in practice.     

A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution

Summary.  A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway–Maxwell–Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway–Maxwell–Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway–Maxwell–Poisson distribution in fitting count data which do not seem to follow the Poisson distribution.     

Improving the Efficiency of the Nelson–Aalen Estimator: the Naive Local Constant Estimator

Abstract.  The Nelson–Aalen estimator is well known to be an asymptotically efficient estimator of the cumulative hazard function, see Andersen et al. ( Statistical models based on counting processes , Springer-Verlag, New York, 1993) among many others. In this paper, we show that the efficiency of the Nelson–Aalen estimator can be considerably improved by using more information in the estimation process than the traditional Nelson–Aalen estimator uses. While our approach results in a biased estimator, the variance improvement is substantial. By optimizing the balance between the bias loss and the variance improvement, we obtain results on the efficiency gain. Several examples for known failure time distributions are used to illustrate these ideas.     

Multivariate normal estimation: the case (n < p)

Estimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.     

Working life expectancies: the case of Finland 1980–2006

Summary.  Working life expectancy is the future time that a person is expected to spend in employment. The paper is concerned with its estimation jointly with the expected times spent in the related states of 'on disability pension' and 'other alive'. The method, which is novel in this field, first estimates year- and age-dependent probabilities of being in the states of interest by large sample multivariate logistic regression. Estimates of probabilities, and subsequently expectancies, are given for the case of Finnish women and men aged 16–64 years for selected years in the period 1980–2001, together with projections for 2006. Since 1996 the decline in the employment of males has largely been due to the increasing popularity of early retirement. It was not due to an increase in disability. There has been no such decline for women, and the working life expectancy for males has been predicted to decline to or to fall below the initially lower figure for females by 2006. Considering that the Finnish population is aging rapidly, these trends could entail serious social and economic consequences for society in the coming years because of a looming shortage in the labour force that could undermine the sustainability of a welfare state.     

Medicine in black and white: BiDil®: race and the limits of evidence-based medicine

When the US Food and Drug Administration licensed the drug BiDil® in June 2005 it was hailed as a significant step towards "personalised prescribing". This is because BiDil® had been patented, tested and approved for use by just one group of patients: those "of African descent". George Ellison examines the statistical evidence that underpinned the development of BiDil® as a "racial drug" and finds it less than satisfactory.