## Bernoulli

- Bernoulli
- Volume 24, Number 3 (2018), 2278-2327.

### Schwarz type model comparison for LAQ models

Shoichi Eguchi and Hiroki Masuda

#### 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.

#### Article information

**Source**

Bernoulli, Volume 24, Number 3 (2018), 2278-2327.

**Dates**

Received: June 2016

Revised: November 2016

First available in Project Euclid: 2 February 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1517540475

**Digital Object Identifier**

doi:10.3150/17-BEJ928

**Mathematical Reviews number (MathSciNet)**

MR3757530

**Zentralblatt MATH identifier**

06839267

**Keywords**

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

#### Citation

Eguchi, Shoichi; Masuda, Hiroki. Schwarz type model comparison for LAQ models. Bernoulli 24 (2018), no. 3, 2278--2327. doi:10.3150/17-BEJ928. https://projecteuclid.org/euclid.bj/1517540475