Could condom stop the AIDS epidemic?
Coupling a branching process to an infinite dimensional epidemic process***
Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence...
Coupling a stochastic approximation version of EM with an MCMC procedure
The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with markovian perturbations are used to establish...
Coupling a stochastic approximation version of EM with an MCMC procedure
The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with Markovian perturbations are used to establish...
Covariance matrix elements estimation: special linear model without and with repeated measurement
Covariance Structure of Principal Components for Three-Part Compositional Data
Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates....
Covariance structure of wide-sense Markov processes of order k ≥ 1
A notion of a wide-sense Markov process of order k ≥ 1, , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of is the k-dimensional process . The covariance structure of is considered in the general case and in the periodic case. In the general case it is shown that iff is a k-dimensional WM(1) process and iff the covariance function of has the triangular property....
Cramer Type Large Deviations for Studentized U-Statistics.
Critères de classification sur des données hétérogènes
Criteria for optimal design of small-sample experiments with correlated observations
We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimators. Then we show that an approximation of MSE via Fisher information matrix is possible, even for small...
Criterio de comparación de experimentos basado en la información generalizada.
En este trabajo se estudia el criterio de comparación de experimentos en una medida de información generalizada definida por De Groot (1962). Se define el criterio, se estudian sus propiedades y se obtienen diversas relaciones con los criterios de suficiencia. Al estar el estudio restringido a espacios paramétricos finitos, los resultados de mayor interés corresponden a las diversas relaciones obtenidas con el criterio de Blackwell. Debido al gran número de casos particulares que la medida de información...
Criterio de maximización de la quietud esperada (invariante frente a traslaciones respecto a las utilidades).
In this paper we start from the following situation: a decision maker wants information about a certain parameter space for which he has a set of random variables with probability distribution depending on an unknown paremeter belonging to the mentioned space. Generally, we assume that the decision maker may observe values of any experiment but not of two simultaneous ones. This reason makes a comparison between them indispensable to choose the most appropriate for his objectives.Through the article...
Criterio para detectar outliers en poblaciones normales bivariantes.
Damos un procedimiento de detección de outliers para muestras procedentes de poblaciones normales bivariantes, que viene dado por el cuadrado de la distancia entre matrices de sumas de cuadrados y sumas de productos de observaciones muestrales, la cual se ha obtenido a partir de la forma métrica diferencial de Maas.
Criterion for an approximation of variance components in regression models
Criterion of maximizing the expected quietness (invariant by homotethies in relation to the utilities)
Criterios de selección de reglas de decisión con observaciones continuas.
Critical values of Fisher's and Siegel's test
Croisements, ordres et ultramétriques
La représentation visuelle d'une hiérarchie induit un ordre sur les singletons. Si l'on désire représenter la même hiérarchie en tenant compte de contraintes extérieures (ordre des singletons induit par une autre hiérarchie, une partition, un indice de dissimilarité, par exemple) des croisements peuvent apparaître. Il y a un croisement dans la représentation visuelle d'une hiérarchie quand une branche horizontale (associée à un palier) est coupée par une branche verticale associée à un singleton....
Cross additivity - an application
We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility...
Cross clustering of contingency table with multinomial laws.