Contributions of Professor Hirotugu Akaike in Statistical Science

Abstract

Professor Hirotugu Akaike was awarded the 2006 Kyoto Prize for “his major contribution to statisticalscience and model ing with the Akaike Information Criterion (AIC)”. In 1973, he proposed the AIC as a naturalextension of the log-likelihood. The most natural way of applying the AIC is to use it as the model selection or order selection criterion. In the MAICE (minimum AIC estimation) procedure, the model with the minimum value of the AIC is selected as the best one among many possible models. This provided a versatile procedure for statistical modeling that is free from the ambiguities inherent in application of the hypothesis test procedure. However, the impact of the AIC is not limited to the realization of an automatic model selection procedure, and it eventually led to a paradigm shift in statisticalscience. In conventionalstatisticalinference, the theories of estimation and test are developed under the assumption of the presence of a true model. However, in statistical modeling, the model should be constructed based on the entire knowledge such as the established theory, empirical facts, current observations and even the objective of the analysis. Prof. Akaike gave a practical answer to the selection of the prior distribution of the Bayes model. Due to the development of information technologies, we can now access to huge amounts of data in various fields of science and social life. In this information and knowledge society, the Bayes modelis becoming a key technology. In this article, we shall look back at his research in five stages, namely, the launching period, frequency domain time series analysis, time series modeling, AIC and statistical modeling and Bayes modeling (Parzen et al. (1998)). It should be noted here that the reader will notice that his research was always performed based on the needs of researchers in the real-world.