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In is presented some methods and strategies for detectiong and estimating the locations of weak changes in the mean of classe of a Conditional Heteroscedastic AutoRegressif Non-linear model (CHARN) models. We present the results of some simulations for illustrating these methods which are apply to detecting changes in Covid-19 data., Dans sont présentées des méthodes et stratégies pour détecter et estimer les localisations des ruptures dans la moyenne d'une grande classe de modèle autoregressifs conditionnellement non-linéaire. Nous faisons des simulations pour illustrer ces méthodes et les appliquerà la détection des ruptures dans des données du Covid-19. Mots-clés. Séries chronologiques, Ruptures, Données du Covid-19 en France.

International audience

We study a likelihood ratio test for detecting multiple {\it weak} changes in the mean of a class of CHARN models. The locally asymptotically normal (LAN) structure of the family of likelihoods under study is established. It results that the test is asymptotically optimal, and an explicit form of its asymptotic local power is given as a function of candidates change locations and changes magnitudes. Strategies for weak change-points detection and their locations estimates are described. The estimates are obtained as the time indices maximizing an estimate of the local power. A simulation study shows the good performance of our methods compared to some existing approaches. Our results are also applied to three sets of real data., 45 pages, 3 figures, 5 tables, Latex; typos corrected, references added, algorithms improved, tables added

International audience; We derive an empirical poverty index containing most of those proposed in the literature. Then, we study its asymptotic behavior by using empirical processes theory. From the results obtained, we derive a Wald-type test for comparing a vector of theoretical poverty indices to a vector of reference indices. We study the test statistic under the null hypothesis of equality, fixed alternatives, and a sequence of local alternatives. A simulation experiment conducted shows that our test performs well for exponential and Pareto data.

We study a likelihood ratio test for detecting small breaks in the mean of CHARN models. We show that in the case the parameters of model are assumed to be known, the test is asymptotically optimal and we give an explicit form of its asymptotic power. In the case the parameters are unknown, replacing them by suitable estimators, the test remains optimal and an explicit expression of the local power is provided. A simulation study will evaluate the performance of the method., Nous étudions un test du rapport de vraisemblance permettant de détecter les ruptures discrètes dans la moyenne des modèles CHARN. Nous montrons que dans le cas où les paramètres du modèle sont connus, le test est asymptotiquement optimal et nous donnons une forme explicite de sa puissance asymptotique. Dans le cas où les paramètres sont inconnus, en les remplaçant par des estimateurs appropriés, le test reste optimal et une expression explicite de la puissance locale est donnée. Uneétude de simulation permettra d'évaluer les performances de la méthode. Mots-clés. Séries chronologiques, test du rapport de vraisemblance, optimalité, contiguïté, rupture.. .

International audience

International audience; A locally asymptotically optimal test is constructed for log-return processes. The behavior of the test statistic is studied under the null and under a sequence of local alternatives. A local asymptotic normality (LAN) result is previously established. Applying the test to log-return data, one rejects the hypothesis that they are independent and identically distributed (iid).

Introduction:In this article, we only focus on the probability distributions of the breakdown time whose causes are known, and we consider a partition of the observations into subgroups according to each of the causes as defined in Njamen and Ngatchou [1]. By adapting the stochastic processes developed by Aalen [2, 3], we derive a Kaplan-Meier [4] nonparametric estimator for the survival function in competiting risks.Result & Discussion:In a region where there is at least one observation, we prove on one hand that this new nonparametric estimator is unbiased in competiting risk and on the other hand, using the Lenglart inequality, we establish its uniform consistency in competiting risks.

A locally asymptotically optimal test is constructed for log-return processes. The behavior of the test statistic is studied under the null and under a sequence of local alternatives. A local asymptotic normality (LAN) result is previously established. Applying the test to log-return data, one rejects the hypothesis that they are independent and identically distributed (iid).

International audience

International audience

International audience

International audience