A0558
Title: Quasi likelihood analysis and model selection for stochastic processes
Authors: Nakahiro Yoshida - University of Tokyo (Japan) [presenting]
Abstract: The quasi likelihood analysis (QLA) gives a basis of statistical inference for stochastic processes. The polynomial type large deviation (PLD) inequality featuring in the QLA provides estimates of the tail of the quasi likelihood random field and hence $L_p$-boundedness of the quasi maximum likelihood estimator and the quasi Bayesian estimator. The QLA is one of the mathematical fundamentals in the theory of information criteria for model selection. The PLD inequality follows from only the local asymptotic quadratic structure of the quasi log likelihood function. The QLA can extend to the penalized QLA in an abstract manner, keeping PLD. Consequently, for example, $L_p$-boundedness of the penalized estimator and a precise estimate of the probability of selection consistency are obtained. The penalized QLA so obtained can be applied with high universality to various dependent structures. We will discuss applications of the QLA to information criteria and penalized methods for estimation of point processes and diffusion type processes.
