Introduction and Preliminaries
An outline of the stochastic inference problem, in general terms, is presented in this chapter. This includes the notions of distinctness of hypotheses to be tested as well as the associated parameter estimation from observations. Then, how both these questions can be unified into a broad framework of a decision theory is discussed. These ideas will be elaborated later on and then their application to various classes of stochastic processes will take the center stage.
KeywordsLoss Function Inference Problem Inference Theory Bibliographical Note Composite Hypothesis
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- Fisher, R. A. “On the mathematical foundations of theoretical statistics,” Phil. Trans. Roy. Soc. (London, Ser. A),222 (1921), 309–368.Google Scholar
- On the orthogonality of independent increment processes,“ In Topics in Probability,NYU Courant Inst. (1973), 93–111. Neyman, J., and Pearson, E. S.Google Scholar
- Dvoretzky, A., Kiefer, J., and Wolfowitz, J. “Sequential decision problems for processes with continuous time parameter: problems of estimation,” Ann. Math. Statist. 24 (1953) 403–415.Google Scholar