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.     

On the detection of changes in autoregressive time series I. Asymptotics

Various test statistics are discussed which can be used for detecting changes in the parameters of an autoregressive time series. In this first part of our study, the limiting behavior of the test statistics is derived under the null hypothesis of no change as well as under alternatives. In a forthcoming second part of our investigation, these asymptotic results will be compared to some corresponding bootstrap procedures, and a small simulation study will be conducted.     

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.     

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.     

Optimal discrimination designs for exponential regression models

We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw [1995. Robust sampling designs for compartmental models under large prior eigenvalue uncertainties. Math. Comput. Biomed. Appl. 181–187] or Gibaldi and Perrier [1982. Pharmacokinetics. Marcel Dekker, New York]. We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of support points of locally optimal discrimination designs than those given by Caratheodory's Theorem. These results greatly facilitate the numerical construction of optimal designs. Various examples of optimal designs are then presented and compared to different other designs. Moreover, to protect the experiment against misspecifications of the nonlinear model parameters, we adapt the design criteria such that the resulting designs are robust with respect to such misspecifications and, again, provide several examples, which demonstrate the advantages of our approach.     

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.     

Occupancy numbers for dynamic heterogeneous populations: Estimate of particles lifetimes

A dynamic model of a heterogeneous population is studied. Particles belonging to a population are divided, at every time t, into a finite number of classes according to their types and the partition changes over time. The role of the occupancy numbers, namely the cardinality of each class, is highlighted. The relationship between the stochastic process of occupancy numbers and the process of particle types is analyzed. The main goal of this paper is the estimation of the lifetime of each particle at a given time t, when the observed data are the history of the process of the number of dead particles up to t. Furthermore, a discrete time approximation of the filter is given.     

Bayesian mixture modeling for spatial Poisson process intensities,with applications to extreme value analysis

We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days.