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Gaussian model selection

Lucien Birgé, Pascal Massart (2001)

Journal of the European Mathematical Society

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,...

Goodman-Kruskal Measure of Association for Fuzzy-Categorized Variables

S. M. Taheri, Gholamreza Hesamian (2011)

Kybernetika

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 p -value. The applicability of the proposed approach is explained using a numerical example.

Hypotheses testing with the two-parameter Pareto distribution on the basis of records in fuzzy environment

Ali Reza Saeidi, Mohammad Ghasem Akbari, Mahdi Doostparast (2014)

Kybernetika

In problems of testing statistical hypotheses, we may be confronted with fuzzy concepts. There are also situations in which the available data are record statistics such as weather and sports. In this paper, we consider the problem of testing fuzzy hypotheses on the basis of records. Pareto distribution is investigated in more details since it is used in applications including economic and life testing analysis. For illustrative proposes, a real data set on annual wage is analyzed using the results...

Invariance and R-ε criterion.

Julián de la Horra (1986)

Trabajos de Estadística

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.

Francisco Criado Torralba (1983)

Trabajos de Estadística e Investigación Operativa

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.

La distància de l'Eixample.

Michael Greenacre (2002)

Qüestiió

Taking our inspiration from the design of the Eixample district in Barcelona by Ildefons Cerdà, we define a new statistical distance function, called the Eixample Distance. We study some properties of this distance and propose some possible applications.

Le modèle bayésien

Philippe Caillot, Françoise Martin (1972)

Annales de l'I.H.P. Probabilités et statistiques

Les problèmes de la statistique

G. Th. Guilbaud (1996)

Mathématiques et Sciences Humaines

Le texte qu'on va lire est une réimpression du Chapitre VI du Traité de Sociologie (tome premier), publié en 1959 aux Presses Universitaires de France sous la direction de Georges Gurvitch. Celui-ci était en effet assez convaincu de l'importance de la Statistique dans sa discipline pour vouloir qu'une présentation en soit faite dans son Traité. On verra que le parti pris par G. Th. Guilbaudfut non de décrire des techniques de la Statistique en vogue chez les sociologues de cette époque (comme par...

Les P-values comme votes d'experts

Guy Morel (2010)

ESAIM: Probability and Statistics

The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often criticized for the two-sided hypothesis problem. We analyze this practice with a new approach to statistical inference. First we select good decision rules without using a loss function, we call them experts. Then we define a probability distribution on the space...

Likelihood and the Bayes procedure.

Hirotugu Akaike (1980)

Trabajos de Estadística e Investigación Operativa

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.

L'implication statistique, une nouvelle méthode d'analyse de données

Régis Gras, Annie Larher (1992)

Mathématiques et Sciences Humaines

Si le problème de la concomitance de deux variables a et b trouve une partie de sa réponse dans l'étude symétrique de la corrélation ou dans celle de la similarité, celui de l'implication (si a alors b) passe, en revanche, par l'examen d'une relation dissymétrique. Par rapport à une problématique psychologique de complexité, R. Gras, dans sa thèse, a apporté une contribution qui a permis de nombreuses applications de ce type de relation dans des travaux de recherche en psychologie génétique et en...

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