統計的推測理論の深化と進展のヒストリー

摘要

The theoretical development of statistical inference was started by R. A. Fisher in 1920s and contributed by A. Wald, L. LeCam. C. R. Rao, R. R. Bahadur, J. Kiefer, J. Wolfowitz and others in a systematic way in 1950s, and its theory was completed for the present. After that, based on the first order asymptotic theory that had been established until then and under consideration of a general resolution of Fisher's conjecture, the higher order asymptotics has been studied very hard by B. Efron, J. Pfanzagl, J. K. Ghosh, K. Takeuchi and the author among others. In this article, we will trace the history of "deepening" and "progresy" in statistical inference around the development of higher order asymptotic theory.%統計的推測の理論的発展は1920年代のR. A. Fisherの研究に始まり，1950年代頃からA. Wald, L. LeCam, C. R. Rao, R. R. Bahadur, J. Kiefer, J. Wolfowitzらによって体系的に論じられ，一先ずその理論が完成された.その後1970年代になって，それまでの1次の漸近理論を踏まえてFisherの予想の一般的解決も視野に入れて，高次漸近理論の研究がB. Efron.J. Pfanzagl, J. K. Ghosh,竹内啓，筆者らによって精力的に行われた.本稿では高次漸近理論の発展を中心に統計的推測の深化と進展のヒストリーを迪る.