An oracle approach for interaction neighborhood estimation in random fields


Autoria(s): LERASLE, Matthieu; TAKAHASHI, Daniel Y.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

19/04/2012

19/04/2012

2011

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

http://dx.doi.org/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