1989 Fiscal Year Final Research Report Summary
Research on the mathematical structure of statistical inference and its application
| Project/Area Number |
63302006
|
|---|
| Research Category |
Grant-in-Aid for Co-operative Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
HIROTSU Chihiro Univ. of Tokyo, Fac. of Tech., Professor, 工学部・計数工学科, 教授 (60016730)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TANEMURA Masami Inst. of Statistical Mathematics, Associate Professor, 助教授 (80000214)
SIBUYA Masaaki Keio Univ., Fac. of Sci. and Tech., Professor, 理工学部, 教授 (20146723)
SHIBATA Ritei Keio Univ., Fac. of Sci. and Tech., Associate Professor, 理工学部, 助教授 (60089828)
KUDO Akio Kyushu Univ., Fac. of Sci., Professor, 理学部, 教授 (00037144)
KARIYA Takeaki Hitotsubashi Univ., Inst. of Economic Research, Professor, 経済研究所, 教授 (70092624)
|
|---|
| Project Period (FY) |
1988 – 1989
|
| Keywords | Geometrical structure of statistical inference / Design and analysis of experiments / Nonstationary and nonlinear time series / Robust estimation / Multivariate analysis / Company-wide quality control / Spatial statistics / Statistical computing |
|---|
| Research Abstract |
It is usual approach of statistics to develop a unified theory through a deep insight into the mathematical structure abstracted from to practical problems in a real field. On the other hand on application the theory should be modified to meet various restrictions intrinsic to the real field which it its applied. Their unification and specification is essential in developing a statistical theory. This research in particularly concerned with this sort of interactions between theory and application and has been successfully fulfilled to obtained a large number of theoretical and methodological result.
The theoretical works performed are 1 New theory of estimation, tests and asymptotics based on the geometrical structure of the statistical inference.. 2 New theory of design and analysis of experiments including the orthogonal array, the balanced array and some incomplete block designs. 3 Theory of nonnormal continuous distributions for positive random variables such as from the concentrati
… More
on, the price and the survival data. 4 New methodology for a nonstationary and nonlinear time series. 5 New methodology for the multivariate analysis including the multiple regression analysis and the multidimensional scaling.
Applied works intrinsic to some particular field are 1 New methodology in the industry corresponding to its quick development technique and in new mathematics and also to the new concept of company-wide quality control which emphasize creating an attractive quality in earlier stage such as planning or design rather than in manufacturing or inspection processes. 2 New methodology in medicine which is characterized by the large deviations of measurement from subject to subject, by the difficulty of keeping circumstances constant in repeating observations and also by many sorts of incomplete observations. 3 Application of theory of spatial statistics to seismology, geology and to destruction physics. Finally we got some useful results in statistical computing including smoothing techniques and resampling procedures. Less
|
