An oracle approach for interaction neighborhood estimation in random fields
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
19/04/2012
19/04/2012
2011
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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. FAPESP[2009/09494-0] FAPESP[2008/08171-0] |
Identificador |
ELECTRONIC JOURNAL OF STATISTICS, v.5, p.534-571, 2011 1935-7524 http://producao.usp.br/handle/BDPI/16708 10.1214/11-EJS618 |
Idioma(s) |
eng |
Publicador |
INST MATHEMATICAL STATISTICS |
Relação |
Electronic Journal of Statistics |
Direitos |
openAccess Copyright INST MATHEMATICAL STATISTICS |
Palavras-Chave | #Ising model #model selection #computationally efficient algorithm #MODEL SELECTION #REGRESSION #PENALTIES #TOPOLOGY #NETWORK |
Tipo |
article original article publishedVersion |