MODERN DEVELOPMENT OF STATISTICAL METHODS

Publisher Summary This chapter discusses the use of the minimum akaike information criterion estimation (MAICE) procedure and its conceptual generalization, the entropy maximization principle, in relation to the problem of stochastic system identification. The most important contribution of MAICE is the clarification of the importance of modeling. The systematic approach to the parameter and structure estimation realized by MAICE makes it almost unnecessary to spend researchers' time for the search of ad hoc procedures. The explicit use of likelihood in MAICE makes it possible to provide clear-cut answers to problems which so far have been treated rather unsystematically. A real system may have various possible choices for its model. A Gaussian AR model can approximate a stationary Gaussian process arbitrarily closely by increasing the order. As the maximum likelihood computation for this model reduces, at least approximately, to the least squares computation, this explains why the so-called least squares method can generally be useful for the identification of stochastic systems.

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