A multivariate version of Gini's rank association coefficient

In this paper, we introduce a multivariate generalization of the population version of Gini's rank association coefficient, giving a response to this open question posed in [4]. We also study some properties of this version, present the corresponding results for the sample statistic, and provide several examples.     

On Christensen's conjecture

In this paper we give solution to a conjecture appearing in Christensen (1997, p. 360) in relation to the definitions of standardized residuals in loglinear models. Work done when he was visiting as the Distinguished Lukacs Professor on leave from the Complutense University of Madrid. An erratum to this article is available at .     

Two-stage Huber estimation

In this paper we propose a new robust estimator in the context of two-stage estimation methods directed towards the correction of endogeneity problems in linear models. Our estimator is a combination of Huber estimators for each of the two stages, with scale corrections implemented using preliminary median absolute deviation estimators. In this way we obtain a two-stage estimation procedure that is an interesting compromise between concerns of simplicity of calculation, robustness and efficiency. This method compares well with other possible estimators such as two-stage least-squares (2SLS) and two-stage least-absolute-deviations (2SLAD), asymptotically and in finite samples. It is notably interesting to deal with contamination affecting more heavily the distribution tails than a few outliers and not losing as much efficiency as other popular estimators in that case, e.g. under normality. An additional originality resides in the fact that we deal with random regressors and asymmetric errors, which is not often the case in the literature on robust estimators.     

Evaluation of multilevel decision trees

The evaluation of decision trees under uncertainty is difficult because of the required nested operations of maximizing and averaging. Pure maximizing (for deterministic decision trees) or pure averaging (for probability trees) are both relatively simple because the maximum of a maximum is a maximum, and the average of an average is an average. But when the two operators are mixed, no simplification is possible, and one must evaluate the maximization and averaging operations in a nested fashion, following the structure of the tree. Nested evaluation requires large sample sizes (for data collection) or long computation times (for simulations).     

Minimum contrast estimation of random processes based on information of second and third orders

This paper presents the results on consistency and asymptotic normality of a class of minimum contrast estimators for random processes with short- or long-range dependence based on the second- and third-order cumulant spectra. Asymptotic properties of sample spectral functionals of second and third orders, which are of independent interest in view of their possible use for nonparametric estimation of processes with short- or long-range dependence, are also provided.     

Wilcoxon–Mann–Whitney test for stratified samples and Efron's paradox dice

Two-treatment multi-center clinical trials are the most common type of clinical trials in practice. The aim of this paper is to discuss a curious property of certain standard nonparametric procedures used in the analysis of such clinical trials. Different analyses of a simulated data example are presented, which lead to contrasting and surprising results. The source of the potentially misleading outcome is then explored while relating the simulated data with the concept of Efron's paradox dice and the notion of nontransitivity. With the root of the problem established, an alternate nonparametric method from the literature is shown to address the problem. Finally, pointing out an interpretational concern of using the alternate procedure, a modification to this procedure is also suggested and corresponding theoretical results are presented.     

Estimating the distribution of one-dimensional discrete scan statistics viewed as extremes of 1-dependent stationary sequences

Discrete one-dimensional scan statistics can be viewed as extremes of 1-dependent stationary sequences. A result of Haiman [1999. First passage time for some stationary processes. Stochastic Process. Appl. 80, 231–248] provides approximations of the distributions of extremes of 1-dependent stationary sequences together with sharp bounds for the corresponding errors. We apply this result to scan statistics generated by Bernoulli r.v.'s and to the charge problem.     

Optimality and bias of some interpolation and extrapolation designs

We consider interpolation and extrapolation designs with controlled bias. A consistent estimate of an upper bound of the bias is presented. The estimate of some extrapolated value is obtained in a two-stage procedure. The first one provides an estimate of some interpolated value. The second one uses a Taylor expansion around this point. This procedure yields a new type of designs. We discuss their optimality properties with respect to the variance and the bias.     

A graphical summary of disparities in health care and related summary measures

In order to assess the effectiveness of government programs designed to reduce disparities in the health care minority groups receive relative to the majority white population, a proper statistical measure should be used. This article proposes a measure of and its accompanying graph, which is readily interpretable and is not affected by the number of minority subgroups examined.     

Bayesian design in queues: An application to aeronautic maintenance

We exploit Bayesian criteria for designing M/M/c//r$M/M/c//r$ queueing systems with spares. For illustration of our approach we use a real problem from aeronautic maintenance, where the numbers of repair crews and spare planes must be sufficiently large to meet the necessary operational capacity. Bayesian guarantees for this to happen can be given using predictive or posterior distributions.