事象の発生数のモデルとしてポアソン分布が当てはまらない事態において,一般化ポアソン分布やポアソン分布の混合分布がこれまで提案されている.これらのモデルはポアソン分布をより一般化したものであるが,ある確率分布を持つ均質な観測個体の母集団を想定している.一方,このような集団自体が変化・相違し,かつそれらが,集団の変化・相違を記述する説明変数により,決定されるという状況のモデルを当論文は提案している.すなわち,一般化ポアソン分布とポリア-エゲンベルガー分布のパラメータが説明変数の関数として構造化されているモデルである.適用例では,提案されたモデルが知能検査における誤答数の分布の,年齢とともに変化・相違する状況を記述することに役立つことを示す.

抄録全体を表示

入学試験は受験生の能力を測定するものであるが,誤差を伴う.ここでは2段階選抜における誤差(逆にいえば正確さ)を計算し,全体の誤差を最小にするにはどのような試験を行えばよいかを論ずる.定員を分けて合格者を2回にわたって決める分離分割方式の正確さも,2段階選抜に帰着できることを示す.

抄録全体を表示

近年P.Diaconisによって定式化された群の表現論に基づくスペクトル解析法は,様々なタイプの統計的な問題に対し応用が可能であることが筆者らによって示されている.本論文では,テストの正答・誤答データにその手法を適用する.ここで考える群は対称群で,その線型表現の下で不変な部分空間にデータベクトルを射影し,結果の解釈を行なう.細かな数学的議論は他の論文に譲り,主に考え方と結果の解釈の仕方に的を絞り,実例をあげて論述する.

抄録全体を表示

The role of Behaviormetrics is to develop and apply quantitative methodologies for analizing phenomena concerning human behaviors in various fields. To quantify, it is unavoidable to carry out data analysis, sooner or later in the research process. Data analysis, for example, is indispensable for either building or testing models. Consequently, Behaviormetrics has a lot to do with Statistics, the branch of science concerning data and data analysis. Some standard methodologies for statistical data analysis are in particular useful for behaviormetricians. On the other hand, Statistics is undergoing a dramatic change due to the drastic improve ment of both computing environment and the ability of computer itself. First, as a result, with the easy access of computers, the population involving data analysis has been seeing a great increase, not restricted in the fields of natural sciences and technology, but also in the fields of social sciences and humanity. While this increase obviously reflects the availability of many new and easy-to-use softwares, it is also the mighty resource for developing even better softwares. Secondly, the computational revolution exerts direct influences on statistical theories themselves, which may be summarized by the appearence in Statistics in late 70's and early 80' s of so called computer-intensive methods. Some of these methods had been of mere theoretical interest to statisticians, but are ready to be put into practical use now. Some are, of course, totally innovative and unthinkable even 20 or 30 years ago. Here we introduce to our readers some of these new methods for data analysis and discuss their potentials for practical use in near future. We realize that time is needed for practitioners to be at ease with any of these methods. However, this is generally true for any new idea in science and technology, if we look back at the history. For example, factor analysis and many other multivariate statistical methods, once a world out of our reach, are now employed by many of us, as confidently as we handle the more usual t-test or analysis of variance(although we can' t say there exists no problem in the way of application). In the same way, we have sound reason to believe that the day should not be too long for many of these new methods, as powerful and versatile tools, to be applied widely and efficiently. In the sequel, we introduce some of these computer-intensive methods, discuss why and how they are conceived, and indicate the implications for applications. Our discussion is divided into two parts, with each of considerable length and relatively independent of the other. With ample practical examples, Part I gives an easy introduction to sevaral methods for data analysis which utilize computer intensively. Section1deals briefly with the historicalintimate relationship between computation and Statistics. Section 2 concerns nonlinear regression analysis. Section 3 discusses computer-aided design of experiments. It ends with a brief summary in Section 4. Our second part deals with bootstrap, which may be regarded as the typical example of computer-intensive methods in Statistics. This part covers almost all the research work about bootstrap and related studies untill the present day time. The historical background and aquick introduction to bootstrap are given in Section1and2, respectively. The applications of bootstrap to error estimation, mainly biases and variances, and to construction of confidence intervals, are given detailed treatment in Section3 and 4, respectively. Section 5 treats acomparatively less known application, i. e. regression analysis. We are especially ignorant of non-parametric regression. In carrying out bootstrapping, it is of great importance to find efficient resampling schemes, to save time and money, and this is the topic of Section6. Last section, Section7, is devoted to the discussion of many undergoing researches.

抄録全体を表示