## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (192.979 recursos)

Afrika Statistika

1. #### $K$-antithetic variates in Monte Carlo simulation

Nasroallah, Abdelaziz
Standard Monte Carlo simulation needs prohibitive time to achieve reasonable estimations. for untractable integrals (i.e. multidimensional integrals and/or intergals with complex integrand forms). Several statistical technique, called variance reduction methods, are used to reduce the simulation time. In this note, we propose a generalization of the well known antithetic variate method. Principally we propose a $K$−antithetic variate estimator (KAVE) based on the generation of $K$ correlated uniform variates. Some numerical examples are presented to show the improvenment of our proposition.

2. #### Sur le codage barycentrique linéaire par morceaux d'un questionnaire

Bidounga, Rufin
Our study is focused on the research of a coding that would keep as best as can be the real configuration of a questionnaire containing ordered categorical variables which are graded according to approbation. The piecewise barycentric codings with picewisely acting pivots and an active zero describes both an improvement and and a generalisation of the personal equation coding keeping the order of given rating. As we have given to the middle pivot a distinct action on the different belonging functions for the four manners of response, we have established a more refined coding which distinguishes the ways to seperate...

3. #### Étude de l'estimateur de la distance minimale pour des modèles de rupture des processus de Poisson: cas avec simulations

Ba, D. B.; Dabye, A. S.; Diakhaby, A.; Lo, G. S.
Ce travail est consacré aux problèmes d’estimation pour différents modèles de processus de Poisson non homogènes. Nous supposons que la fonction d’intensité du processus de Poisson est discontinue par rapport aux paramètres inconnus. On montre que l’estimateur de la distance minimale est consistant et asymptotiquement normal. Des simulations sont faites pour chaque modèle.

4. #### On optimality of the empirical distribution function for the estimation of the invariant distribution function of a diffusion process

Negri, Ilia
In this work we present some results on the optimality of the empirical distribution function as an estimator of the invariant distribution function of an ergodic diffusion process. The results presented were obtained in different previous works under conditions that are rewritten in a unified form that make those results comparable. It is well known that the empirical distribution function is an unbiased and uniformly consistent estimator for the invariant distribution function of an ergodic diffusion process. It is also an efficient estimator in the sense that the risk of this estimator attains an asymptotic minimax lower bound. In this...

5. #### An approximation for the power function of a semi-parametric test of fit

Boukili Makhoukhi, Mohammed
We consider in this paper goodness of fit tests of the null hypothesis that the underlying distribution function of a sample $F(x)$ belongs to a given family of distribution functions $\scr F$. We propose a method for deriving approximate values of the power of a weighted Cramér-von Mises type test of goodness of fit. Our method relies on Karhunen-Loève expansions on $(0,1)$ for the weighted Brownian bridges.

6. #### Modélisation statistique des données Aleurodicus sur agrume par des lois de Poisson pondérées

Mizère, Dominique
In the paper we have undertaken, with aid of the weighted Poisson distribution, to fit the count data collected in Republic of Congo-Brazzaville and related to a sample of spiraling whitefly Aleurodicus dispersus Russel (Homoptera: aleyrodidae) described by the preimaginal span (from eggs to adult stage) measured on days, the total number of eggs and the laying span. The linear regression issue between these three variables will be discussed as well.

7. #### The asymptotic theory of the poverty intensity in view of extreme value theory for two simple cases

Lo, Gane Samb; Sall, Serigne Touba
Let $Y_1,Y_2\dots$ be independent observations of the income variable of some given population, with underlying distribution $G$. Given a poverty line $Z$, then for each $n\geq 1$, $q=q_n$ is the number of poor in the population. The general form of poverty measures used by economists to monitor the welfare evolution of this population is $$P_n=\frac{1}{a(q)b(n)}\sum^q_{j=1}c(n,q,j)d\left(\frac{Z-Y_{j,n}}{Z}\right).$$ This class includes the most popular poverty measures like the Sen, Shorrocks and Greer-Foster-Thorbecke statistics. We give a complete asymptotic normality theory in the framework of extreme value theory. In this paper, the poverty intensity is studied in two simple cases: Pareto and exponential distributions....

8. #### Temperature stochastic modeling and weather derivatives pricing: empirical study with Moroccan data

Mraoua, Mohammed; Bari, Driss
The main objective of this paper is to present a technique for pricing weather derivatives with payout depending on temperature. We start by using the Principle Component Analysis method to fill missing temperature data. Consequently, the cold and the warm periods were determined on the basis of a “clean” data by using a statistical approach. After that, we use historical data over a sufficient period to apply a stochastic process that describes the evolution of the temperature. A numerical example of a swap contract pricing is presented, using an approximation formula as well as Monte Carlo simulations.

9. #### An Akaike criterion based on Kullback symmetric divergence in the presence of incomplete-data

This paper investigates and evaluates an extension of the Akaike information criterion, KIC, which is an approximately unbiased estimator for a risk function based on the Kullback symmetric divergence. KIC is based on the observed-data empirical log-likelihood which may be problematic to compute in the presence of incompletedata. We derive and investigate a variant of KIC criterion for model selection in settings where the observed-data is incomplete. We examine the performance of our criterion relative to other well known criteria in a large simulation study based on bivariate normal model and bivariate regression modeling.

10. #### Vitesse de convergence de certains estimateurs de Kaplan-Meier de la régression

Gneyou, Kossi Essona
On considère dans cet article des estimateurs à noyau de la régression basés sur des données censurées à droite qui, dans le cas de non censure, sont identiques aux estimateurs à noyau de la régression de Nadaraya-Watson (1964). La vitesse de convergence uniforme presque sûre sur un intervalle fermé et borné est établie pour ces estimateurs. On utilise ensuite une représentation de la régression par une $V C − classe$ mesurable de fonctions et établit une inégalité exponentielle permettant d’avoir la vitesse de convergence uniforme presque sûre du type Földes et Rejtő (1981) de l’estimateur de Kaplan-Meier de la fonction...

11. #### Test of no-effect hypothesis

On se donne une suite de vecteurs aléatoires $(X_1, Y_1), ..., (X_n, Y_n)$ définies sur le mème espace probabilisé $(\Omega, A, P)$. Après avoir considéré l’estimation de la fonction de regression $r (x)$, nous étudions le test d’hypothèse nulle “$r (x) = cste$”, c’est à dire que $X$ n’a pas d’effet en moyenne sur $Y$, dans deux situations où les variables aléatoires $(X_i, Y_i)$ sont indépendantes ou forment un processus stationnaire et $\alpha$−mélangeant. Des lois limites sous diverses alternatives sont obtenues ainsi que des conditions nécessaires et suffisantes de convergence du test. Des simulations sont indiquées.

12. #### Répartition ponctuelle aléatoire des revenus et estimation de l'indice de pauvreté

Dia, Galaye
Nous nous proposons d'étendre dans le cadre des processus ponctuels l'étude des estimateurs classiques des indices de pauvreté. Dans l'étude qui va suivre, nous proposons un estimateur de l'indice de Forster-Greer-Thorbecke.

13. #### Process of random distributions classification and prediction

Emilion, Richard
We define a continuous time stochastic process such that each is a Ferguson-Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case. ¶ We give an application in classifiying moving distributions by proving that the above random distributions are generally mutually orthogonal. The proofs hinge on a theorem of Kakutani.

14. #### Opérateur de Hardy et espaces gaussiens

Ouknine, Youssef; Elhssaini, Youssef
Ce travail est une extention du résultat du deuxième paragraphe dans [2] (et par suite celui de [4]), où on a démontré une représentation Chaotique pour le pont Brownien généralisé; En fait nous allons montrer ici un résultat simailaire pour le pont généralisé du drap Brownien à $n$ paramétres.

15. #### Weighted multivariate Cramér-von Mises-type statistics

Deheuvels, Paul
In this paper, we consider weighted quadratic functionals of the multivariate uniform empirical process. By deriving the Karhunen-Loève expansion of the corresponding limiting Gaussian process, we obtain the asymptotic distribution of these statistics. Our results have direct applications to tests of goodness of fit and tests of independence by Cramér-von Mises-type statistics.

16. #### Modélisation des données de la pauvreté par la famille Singh-Maddala

Haidara, Mohamed Cheikh
Nous abordons la modélisation des données de la pauvreté, en particulier, celles des bases de données sénégalaises de 1996 à 2001, par la famille des fonctions de répartition de Singh-Maddala. Les résultats sont bien meilleurs que l’ajustage classique Lognormal. Ces résultats permettent le calcul fiable des indicateurs de pauvreté en termes d’intervalles de confiance en vue d’un suivi efficace de la pauvreté, un des objectifs du Millénaire pour le développement.

17. #### L'analyse CONCORG simultanée: la méthode CONCORGS

Kissita, Gabriel; Makany, Roger Armand; Mizère, Dominique
The analysis CONCORG is a method that investigates the link between two multi-tables (partitioned sets of variables measured on the same individuals). It allows to detail the contributions of partial sub-tables forming the two tables. CONCORG is an extension of Concor, which itself is an extension of the inter-battery analysis. This new method performs successive determinations of the solution. In this article, we propose three criteria that enables to simultaneously identify solutions. It happens that the three criteria are equivalent to the solution. In this sense, our method, denoted as CONCORGS, is a generalization of CONCORG. Finally, we establish a...

18. #### Optimal portfolios under dynamic shortfall constraints

Akume, Daniel; Luderer, Bernd; Wunderlich, Ralf
Value-at-Risk (VaR), a downside risk measure, has emerged as the industry standard with regulatory authorities enforcing its use in risk measurement and management. Despite its widespread acceptance, VaR is not coherent. Tail Conditional Expectation (TCE), on the other hand, for an underlying continuous distribution, is a coherent risk measures. Our focus in this paper is the dynamic portfolio and consumption choice of a trader subject to a risk limit specified in terms of TCE.

19. #### Computation of spectral gap for a colored disordered lattice gas

Bey Touati, Ali; Zeghdoudi, Halim; Boutabia, Hacène
We consider a system of colored disordered lattice gas in a volume $\Lambda$ of $\mathbb{Z}^d$ which plays an important role in the study of hydrodynamic limit. A new computation method for the canonical measures for such a system has been established in [10]. We use those results and base on them computation method for the related spectral gap which in turn has important application in hydrodynamic.

20. #### Another look at second order condition in extreme value theory

Lo, Gane Samb; Fall, Adja Mbarka
This note compares two approaches both alternatively used when establishing normality theorems in univariate Extreme Value Theory. When the underlying distribution function (df) is the extremal domain of attraction, it is possible to use representations for the quantile function and regularity conditions (RC), based on these representations, under which strong and weak convergence are valid. It is also possible to use the now fashion second order condition (SOC), whenever it holds, to do the same. Some authors usually favor the first approach (the SOC one) while others are fond of the second approach that we denote as the representational one....

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