| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1996: ¥700,000 (Direct Cost: ¥700,000)
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| Research Abstract |
This work is the second step of preceding research which was supported by Grant-in-Aid for Scientific Research of the Ministry of Education with Contract Number 06680293. The aim of this research is to investigate the asymptotic expansion approximation to the probability of misdiscrimination (PMD) on the discriminant analysis for two normal populations II<@D2i@>D2 : N<@D2p@>D2(mu<@D2i@>D2, SIGMA), mu<@D2i@>D2 (]SY.tri-substituted right.[) *, (]SY.tri-substituted right.[) (]SY.di-substituted left.[) 0, i = 1, 2), and to construct an experimental upper pound on the absolute error of the approximation. We often estimate the PMD, which is based on Wald-Anderson's W-rule, by the asymptotic expansion formula because of the difficulty of evaluation for the "exact " PMD.The asymptotic expansion formula is a function of the parameters, that is, the dimension of data p, the sample size n, and Mahalanobis distance DELTA, therefore, we have to seek the domain of the parameter space (p, n, DELTA) which would give the good approximation for the asymptotic expansion formula of PMD.To constitute the domain, we call it "reference domain D", on the first step, we descrive some curves of PMD given by the asymptotic expansion formula, and determine D.For some selected points of (p, n, DELTA) in D, we next estimate the exact PMD by Monte Carlo simulation, and evaluate the absolute error between PMD by asymptotic expansion formula and one by the simulation. Finally, to construct an experimental upper bound U<@D2T@>D2 XI U<@D2T@>D2(p, n, DELTA) = Kp<@D1p@>D1n<@D1lambda@>D1 exp{a(DELTA - 0.6)}(1 + epsilon), (p, n, DELTA) (]SY.tri-substituted right.[) D, we estimate the constants K, a, p, lambda, epsilon by using the same points, we have K = 0.08054, a = -1.49827, p = 0.99678, lambda = -1.99357, epsilon = 1.7836. To check the effectiveness of U<@D2T@>D2, we apply the rest of the
other points in D, we can show the effectiveness of U_T for most of all the points.
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