An oracle approach for interaction neighborhood estimation in random fields

Author(s)

Lerasle, Matthieu ^[1] ; Takahashi, Daniel Y. ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil

• Document type: Journal article
• Source: ELECTRONIC JOURNAL OF STATISTICS; v. 5, p. 534-571, 2011.
• Web of Science Citations: 3

Abstract

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