An oracle approach for interaction neighborhood estimation in random fields

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: ELECTRONIC JOURNAL OF STATISTICS; v. 5, p. 534-571, 2011.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 08/08171-0 - Modelagem de populações de neurônios por sistemas markovianos de muitos componentes com interações de alcance variável
• Beneficiário: Daniel Yasumasa Takahashi
• Linha de fomento: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 09/09494-0 - Reamostragem e seleção de modelos para cadeias estocásticas com memória de alcance variável
• Beneficiário: Matthieu Pierre Lerasle
• Linha de fomento: Bolsas no Brasil - Pós-Doutorado