L'algorithme SEM : un algorithme d'apprentissage probabiliste pour la reconnaissance de mélange de densités
LAMN property for hidden processes : the case of integrated diffusions
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...
LAN and LAMN for systems of interacting diffusions with branching and immigration
L'analyse implicative bayésienne, une méthode pour l'étude des dépendances orientées. II : modèle logique sur un tableau de contingence
Dans Bernard & Charron (1996), nous avons proposé une nouvelle méthode, l'Analyse Implicative Bayésienne (AIB), pour l'étude des dépendances orientées entre deux variables binaires, méthode qui permet de conclure en terme de quasi-implication entre modalités des variables. Nous étendons ici cette méthode au cas d'un tableau de contingence A × B quelconque avec le problème de la mesure du degré de quasi-adéquation des données à un modèle logique donné. Au niveau descriptif, la méthode repose...
L'analyse implicative bayésienne, une méthode pour l'étude des dépendances orientées. I : données binaires
La réussite à l'épreuve A implique-t-elle, approximativement, la réussite à l'épreuve B ? Parmi les indices descriptifs proposés pour mesurer de telles dépendances orientées, nous considérons l'indice H de Loevinger, qui s'exprime simplement en termes des taux de liaison entre modalités. A partir de cet indice, nous définissons les notions de quasi-implication, de quasi-équivalence et de quasi-indépendance dans un tableau de contingence 2 x 2. Cependant, les méthodes inductives correspondantes,...
Large adaptive estimation in linear regression model. I. Consistency
Large deviations for quasi-arithmetically self-normalized random variables
We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means, we generalize the large deviation result on self-normalized statistics that was obtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations. Ann. Probab. 25 (1997) 285–328]. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.
Large Sample Estimation of Pareto Quantiles Using Selected Order Statistics.
Large Sample Estimation Strategies for Eigenvalues of a Wishart Matrix.
Least empirical risk procedures in statistical inference
We consider the empirical risk function (for iid ’s) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.
Least squares approximation in Bayesian analysis.
This paper presents in a simple and unified framework the Least-Squares approximation of posterior expectations. Particular structures of the sampling process and of the prior distribution are used to organize and to generalize previous results. The two basic structures are obtained by considering unbiased estimators and exchangeable processes. These ideas are applied to the estimation of the mean. Sufficient reduction of the data is analysed when only the Least-Squares approximation is involved....
Least squares estimator consistency: a geometric approach
Consistency of LSE estimator in linear models is studied assuming that the error vector has radial symmetry. Generalized polar coordinates and algebraic assumptions on the design matrix are considered in the results that are established.
Least Squares Estimator for Regression Models with some Deterministic Time Varying Parameters.
Least squares for practitioners.
Les estimateurs robustes sont-ils vraiment robustes en pratique ?
Likelihood and parametric heteroscedasticity in normal connected linear models
A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.
Likelihood and quasi - likelihood estimation of transition probabilities
In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.
Likelihood and the Bayes procedure.
In this paper the likelihood function is considered to be the primary source of the objectivity of a Bayesian method. The necessity of using the expected behaviour of the likelihood function for the choice of the prior distribution is emphasized. Numerical examples, including seasonal adjustment of time series, are given to illustrate the practical utility of the common-sense approach to Bayesian statistics proposed in this paper.
Likelihood for random-effect models (with discussion).
For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows influence from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, statistical and computational efficiency. We introduce an extended likelihood framework and discuss why...
Likelihood ratio inequalities with applications to various mixtures