Application of Akaike's Information Criterion to the Selection of Optimum Order for Stochastic Systems of Hierarchically Expanded Regression Type
Yasuo Mitani, Mitsuo Ohta · International Symposium on Information Theory and its Applications · 1994
In order to study systematically the complicated actual stochastic phenomena in the living acoustic and vibration environments, some kinds of hierarchical probability expressions of infinite series expansion type have been often employed theoretically at the stalling point of analysis. Paying attention to the definite sample size of observed data and the inevitable estimation error of each distribution parameter, we must find reasonably an optimum order of the theoretical expansion terms. In this paper, a reasonable method for selecting this optimum order of expansion terms in the previously reported regression analysis method of an extended type is proposed by introducing the well-known Akaike's information criterion (abbr., AIC). Here, from the practical point of view, we regard approximately the remaining higher order expansion terms after employing an optimum number of the expansion term as some meaningless error information. The effectiveness of the proposed method is experimentally confirmed by applying it to the simulation experiment and the actual data in a complicated acoustic environment.