Schwarz type model comparison for LAQ models

Shoichi Eguchi, Hiroki Masuda

Research output: Contribution to journalArticle

4 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 1 2018

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Model Comparison
Multiscaling
Quasi-likelihood
M-estimator
Information Matrix
Approximate Model
Bayesian Model
Model Selection
Process Model
Stochastic Model
Computational Cost
Stochastic Processes
Deduce
Likelihood
Asymptotic Behavior
Numerical Experiment
Model
Statistics
Experiment

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Schwarz type model comparison for LAQ models. / Eguchi, Shoichi; Masuda, Hiroki.

In: Bernoulli, Vol. 24, No. 3, 01.08.2018, p. 2278-2327.

Research output: Contribution to journalArticle

Eguchi, Shoichi ; Masuda, Hiroki. / Schwarz type model comparison for LAQ models. In: Bernoulli. 2018 ; Vol. 24, No. 3. pp. 2278-2327.
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