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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

An oracle approach for interaction neighborhood estimation in random fields

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Lerasle, Matthieu [1] ; Takahashi, Daniel Y. [1]
Total Authors: 2
[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil
Total Affiliations: 1
Document type: Journal article
Source: ELECTRONIC JOURNAL OF STATISTICS; v. 5, p. 534-571, 2011.
Web of Science Citations: 4

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study. (AU)

FAPESP's process: 09/09494-0 - Bootstrap and model selection for stochastic chains with memory of variable length
Grantee:Matthieu Pierre Lerasle
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 08/08171-0 - Modeling populations of neurons with multicomponent systems with variable range interactions
Grantee:Daniel Yasumasa Takahashi
Support type: Scholarships in Brazil - Post-Doctorate