| Project/Area Number |
01530013
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
統計学
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
TAKAHASHI Hajime Hitotsubashi Univ., Economics Dept., Professor, 経済学部, 教授 (70154838)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Hajime Hitotsubashi Univ., Economics Dept., Professor (70154838)
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| Project Period (FY) |
1989 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Structual change / Sequential analysis / Renewal theory / Cusum test / RENEWAL THEORY |
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| Research Abstract |
We obtained the asymptotic expansions of the expected values of the truncated stopping time and the sample mean of the randomly stopped sequence of independent normally distributed random variables. The results may be applied to obtain the statistical characteristics of the Cusum test for detecting the mean changes, such as error probabilities and the expected sample sizes. The results may be used to estimate the time at which the change occurs after having rejected the null hypothesis of no mean changes. We also applied the Cusum test for the detection of the mean change to the Gamma-mormal mixture model which is suitable for the data with heavier tail than that of the normal distribution. And recent empirical studies of the Financial Time Series show that the underlying distribution tends to have bigger kurtosis. We also applied the method to obtain the similar sequential procedure for detecting the variance change, for the variance may be more important in practice. We used Brownian motion approximation to obtain the probabilities as a first step. We are now working to get the more accurate results by using the (nonlinear) renewal theory with which we will evaluate the asymptotic distribution of the excess over the boundaries. We believe that we have obtained somehow satisfactory results for the detection of the mean change of the sequence of the independent random variables. But the case for the time series data is just started and have not got any satisfactoryresults yet. Although some results concerning the detection of the change of variance was obtained, we are still long way up to the final goal.
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