Titlebook: Stochastic Processes; Inference Theory M. M. Rao Book 20001st edition Springer Science+Business Media Dordrecht 2000 Likelihood.Mathematica

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alance the criteria on some common scale. The principle “first things first” is at the heart of any hierarchical procedure and one may ask for the reasons people are applying it. Beside empirical investigation, an answer may also be given by looking analytically for possible appealing features which

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Parameter Estimation and Asymptotics,parameters. That involves various classes of loss functions, and the study concentrates on certain desirable properties of estimators which are (known) functions of random variables. These include a detailed mathematical analysis of Bayes and maximum likelihood estimation as well as (nonlinear) pred

Projection

Inference for Classes of Processes,nd certain (unbiased) weighted prediction problems together with some calculations of likelihood ratios for processes are detailed. In the discrete indexed cases, an analysis of the asymptotic properties of estimators for some classes is also given. Principles outlined in the preceding chapters on c

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Prediction and Filtering of Processes,neral prediction operations relative to a convex loss function, and its relation to projection operators. This is refined in the next section, for least squares prediction with the Cramér-Hida method. Then Section 3 treats linear filters as formulated by Bochner [2]. The results are specialized and

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Nonparametric Estimation for Processes,tral densities of a class of second order processes. After some necessary preliminaries, we discuss spectral properties of separable, especially harmonizable, processes of second order in Section 1. Then we consider an asymptotically unbiased estimator, and a related function, of the spectral distri