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We will prove a general result about the stochastic expansion of the logarithmic marginal quasi-likelihood associated with a class of locally asymptotically quadratic (LAQ) family of statistical exper...iments. It enables us to make a Bayesian model comparison in a unified manner for a broad range of dependent-data models, thus entailing a far-reaching extension of the classical Schwarz's paradigm with rigorous theoretical foundation. In particular, the proposed quasi-Bayesian information criterion, termed QBIC, prevails even when the corresponding M-estimator is of multi-scaling type and the asymptotic quasi-information matrix is random, as well as the statistical model is misspecified. We will illustrate the proposed method by diffusion-type models.続きを見る
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