Sharp oracle inequalities and slope heuristic for specification probabilities estimation in discrete random fields

Autor(es)

Lerasle, Matthieu ^[1] ; Takahashi, Daniel Y. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, F-06100 Nice - France

^[2] Princeton Univ, Dept Psychol, Inst Neurosci, Princeton, NJ 08648 - USA

• Tipo de documento: Artigo Científico
• Fonte: BERNOULLI; v. 22, n. 1, p. 325-344, FEB 2016.
• Citações Web of Science: 2

Resumo

We study the problem of estimating the one-point specification probabilities in non-necessary finite discrete random fields from partially observed independent samples. Our procedures are based on model selection by minimization of a penalized empirical criterion. The selected estimators satisfy sharp oracle inequalities in L-2-risk. We also obtain theoretical results on the slope heuristic for this problem, justifying the slope algorithm to calibrate the leading constant in the penalty. The practical performances of our methods are investigated in two simulation studies. We illustrate the usefulness of our approach by applying the methods to a multi-unit neuronal data from a rat hippocampus. (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
• Modalidade de apoio: 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
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado