Hierarchical Bayesian Estimation of the Number of Visits to the Generalist in 2002/2003 French Health Survey

In our paper we show how to construct a model for one variable in the French Health Survey data set: the number of times an individual visited a generalist in the last twelve months, for which we are interested in estimating the regional means. Then, we test the fit of the model to the data and compare it to other two alternative models. We derive theoretical formulas for the estimates of the twenty-two regional means along with their standard deviations. We compare this to the design-based estimations obtained by INSEE in the case of the five regions with extra sample. We discuss some alternative for future research.small areas, direct and indirect estimations, Markov chains, Gibbs sampling, Metropolis-Hastings algorithm

Prediction of a Small Area Mean for an Infinite Population when the Variance Components Are Random

In this paper, we propose a new model with random variance components for estimating small area characteristics. Under the proposed model, we derive the empirical best linear unbiased estimator, an approximation to terms of order and an estimator whose bias is of order for its mean squared error, where m is the number of small areas in the population.small areas, direct and indirect estimation, infinite population, empirical best linear unbiased predictor

Type and cotype with respect to arbitrary orthonormal systems

Let \on_{k \in \nz} be an orthonormal system on some $\sigma$-finite measure space (\Om,p). We study the notion of cotype with respect to $\Phi$ for an operator $T$ between two Banach spaces $X$ and $Y$, defined by \fco T := \inf $c$ such that \Tfmm \pl \le \pl c \pll \gmm \hspace{.7cm}\mbox{for all}\hspace{.7cm} (x_k)\subset X \pl, where (g_k)_{k\in \nz} is a sequence of independent and normalized gaussian variables. It is shown that this $\Phi$-cotype coincides with the usual notion of cotype $2$ iff \linebreak \fco {I_{\lin}} \sim \sqrt{\frac{n}{\log (n+1)}} uniformly in $n$ iff there is a positive $\eta>0$ such that for all n \in \nz one can find an orthonormal \Psi = (\psi_l)_1^n \subset {\rm span}\{ \phi_k \p|\p k \in \nz\} and a sequence of disjoint measurable sets (A_l)_1^n \subset \Om with \int\limits_{A_l} \bet \psi_l\rag^2 d p \pl \ge \pl \eta \quad \mbox{for all}\quad l=1,...,n \pl. A similar result holds for the type situation. The study of type and cotype with respect to orthonormal systems of a given length provides the appropriate approach to this result. We intend to give a quite complete picture for orthonormal systems in measure space with few atoms

Fully differential NNLO computations with MATRIX

We present the computational framework MATRIX which allows us to evaluate fully differential cross sections for a wide class of processes at hadron colliders in next-to-next-to-leading order (NNLO) QCD. The processes we consider are $2\to 1$ and $2\to 2$ hadronic reactions involving Higgs and vector bosons in the final state. All possible leptonic decay channels of the vector bosons are included for the first time in the calculations, by consistently accounting for all resonant and non-resonant diagrams, off-shell effects and spin correlations. We briefly introduce the theoretical framework MATRIX is based on, discuss its relevant features and provide a detailed description of how to use MATRIX to obtain NNLO accurate results for the various processes. We report reference predictions for inclusive and fiducial cross sections of all the physics processes considered here and discuss their corresponding uncertainties. MATRIX features an automatic extrapolation procedure that allows us, for the first time, to control the systematic uncertainties inherent to the applied NNLO subtraction procedure down to the few permille level (or better).Comment: 76 pages, 2 figures, 11 table