1991 Fiscal Year Final Research Report Summary
On the discrimination, regression and principal component analysis on the hypersphere and graphical analysis
| Project/Area Number |
02630013
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Economic statistics
|
|---|
| Research Institution | Hitotsubashi University |
|---|
Principal Investigator |
TAYAKAWA T. Hitotsubashi University Dept. of Economics, Professor., 経済学部, 教授 (00000183)
|
|---|
| Project Period (FY) |
1990 – 1991
|
| Keywords | Langevin population / concentration parameter / Robustness / Likelihood ratio criterion / Homogeneity / Asymptotic form / Discriminant analysis / Principal component |
|---|
| Research Abstract |
In this research we have considered the distribution problems of some tests statistics for testing parameters of Langevin population on the sphere.
Homogeneity of parameters of k Langevin populations are fundamental for handling the discriminant analysis and principal component analysis. We have given the asymptotic expansion of the distribution of the likelihood ration criterion for testing the momogeneity of concentration parameters and mean directions of k Langevin populations.
We also studied the homogeneity of parameters of k populations for which the probability (density) functions satisfy some regularity condition. We gave the asymptotic expansion of the distribution of the likelihood ratio criterion of this test up to the order 1/n, where n is the sample size.
|
