Schwarz type model comparison for LAQ models

Shoichi Eguchi, Hiroki Masuda

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

For model-comparison purpose, we study asymptotic behavior of the marginal quasi-log likelihood associated with a family of locally asymptotically quadratic (LAQ) statistical experiments. Our result entails a far-reaching extension of applicable scope of the classical approximate Bayesian model comparison due to Schwarz, with frequentist-view theoretical foundation. In particular, the proposed statistics can deal with both ergodic and non-ergodic stochastic process models, where the corresponding M-estimator may of multi-scaling type and the asymptotic quasi-information matrix may be random. We also deduce the consistency of the multistage optimal-model selection where we select an optimal sub-model structure step by step, so that computational cost can be much reduced. Focusing on some diffusion type models, we illustrate the proposed method by the Gaussian quasi-likelihood for diffusion-type models in details, together with several numerical experiments.

Original languageEnglish
Pages (from-to)2278-2327
Number of pages50
JournalBernoulli
Volume24
Issue number3
DOIs
Publication statusPublished - Aug 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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