Gamma-minimax estimators for the parameters of a multinomial distribution
Gamma-minimax estimators in the exponential family [Book]
Gaussian model selection
Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...
Generalized information criteria for Bayes decisions
This paper deals with Bayesian models given by statistical experiments and standard loss functions. Bayes probability of error and Bayes risk are estimated by means of classical and generalized information criteria applicable to the experiment. The accuracy of the estimation is studied. Among the information criteria studied in the paper is the class of posterior power entropies which include the Shannon entropy as special case for the power . It is shown that the most accurate estimate is in this...
Generalized regression estimation for continuous time processes with values in functional spaces
We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination'' (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the...
Goodman-Kruskal Measure of Association for Fuzzy-Categorized Variables
The Goodman-Kruskal measure, which is a well-known measure of dependence for contingency tables, is generalized to the case when the variables of interest are categorized by linguistic terms rather than crisp sets. In addition, to test the hypothesis of independence in such contingency tables, a novel method of decision making is developed based on a concept of fuzzy -value. The applicability of the proposed approach is explained using a numerical example.
Graphical models for hierarchical computations in the analysis and design of replications.
How powerful are data driven score tests for uniformity
We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative, in the Gaussian...
Identification de paramètres pour un système excité par des bruits gaussien et poissonien
Inadmissibility of two estimators of reliability in the exponential case
Inference on y >yo by Using a Correlated Variable: A Three Decision Approach.
Information inequalities for the minimax risk of sequential estimators (with applications)
Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential...
Information-theoretic approach to measurement reduction problems
Introduction à la statistique mathématique. I. Modèle d'expérimentation statistique
Introduction à la statistique mathématique. III. Décision statistique
Invariance and R-ε criterion.
The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = {θ1, ..., θn}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule δ, there exists an invariant rule δ' which is either preferred or equivalent to δ. The question raised in this paper is: given that the minimax ordering is a particular case of R-ε ordering, is it possible...
Invariancia de las reglas admisibles y Bayes respecto de transformaciones monótonas.
From an optimality point of view the solution of a decision problem is related to classes of optimal strategies: admissible, Bayes, etc. which are closely related to boundaries of the risk set S such as lower-boundary, Bayes boundary, positive Bayes boundary. In this paper we present some results concerning invariance properties of such boundaries when the set is transformed by means of a continuous monotonic increasing function W.
Invited paper with discussion: Natural Induction: An objective Bayesian approach.
Kostenoptimale Prüfpläne bei einem Problem mit drei möglichen Entscheidungen.
Las f*-divergencias como criterio bayesiano de comparación de experimentos.
In this paper a bayesian criterion for comparing different experiments based on the maximization of the f*-Divergence is proposed and studied. After a general setting of the criterion, we prove that this criterion verifies the main properties that a criterion for comparing experiments must satisfy.