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Chapter 11:
Likelihood and Quasi-Likelihood
In this section the local maximum likelihood approach is introduced as a generalization of the linear LPA. It provides universal tools for designing methods and algorithms for a variety of stochastic models that are different from the standard Gaussian one. This approach combines two different ideas: generalized linear modeling and localization of parametric fitting. In the generalized linear model the parameters of distributions are assumed to be varying and the linear regression is used to fit them. The ML approach is exploited to make the estimation of these parameters relevant to the stochastic properties of the observations [78]. Localization of the ML allows one to relax restrictions imposed by the standard parametric ML. The theory and applications of the local maximum likelihood can be seen in [46], [47], [145], and [219]. The ML gives a general constructive idea of how to design optimal nonlinear estimators corresponding to a given distribution. Let us recall briefly the basic concepts of this powerful statistical approach [164], [174].
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Stochastic processes

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