Open Access
August 2018 Schwarz type model comparison for LAQ models
Shoichi Eguchi, Hiroki Masuda
Bernoulli 24(3): 2278-2327 (August 2018). DOI: 10.3150/17-BEJ928


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.


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Shoichi Eguchi. Hiroki Masuda. "Schwarz type model comparison for LAQ models." Bernoulli 24 (3) 2278 - 2327, August 2018.


Received: 1 June 2016; Revised: 1 November 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839267
MathSciNet: MR3757530
Digital Object Identifier: 10.3150/17-BEJ928

Keywords: approximate Bayesian model comparison , Gaussian quasi-likelihood , locally asymptotically quadratic family , quasi-likelihood , Schwarz’s criterion

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
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