Abstract

The quasi-likelihood analysis (QLA) is a systematic framework for statistical inference for stochastic processes. Based on the polynomial type large deviation inequality, it guarantees the asymptotic properties of the Bayesian estimator, for example. Recently, new applications have been found for various dependent structures such as degenerate diffusion processes and point processes. Besides, the theory has been extended to sparse estimation, and inference for non-identifiable models. We discuss recent developments in the theory of QLA and its applications.