CoInvestigator(Kenkyūbuntansha) 
OOTANI Keiko Hiroshima University, , Department of Dentistry, Research Associate, 歯学部, 助手 (20243587)
SATOH Kenichi Hiroshima University, Research Institute for Radiation Biology and Medicine, Res, 原爆放射能医学研究所, 助手 (30284219)
KANDA Takashi Hiroshima Institute of Technology, Department of Environmetrics, Professor, 環境学部, 教授 (40098679)
FUJIKOSHI Yasunori Hiroshima University, Faculty of Science, Professor, 理学部, 教授 (40033849)

Budget Amount *help 
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1997: ¥2,200,000 (Direct Cost: ¥2,200,000)

Research Abstract 
1) Some inferential problems under an extended growth curve model with several hierarchical withinindividuals design matrices were studied. The model includes the one whose mean structure consists of polynomial growth curves with different degrees. First we considered the case when the covariance matrix is unknown positive definite. We derive a LR test for examining the hierarchical structure for withinindividuals design matrices and a model selection criterion. Next we considered the case when a random coefficients covariance structure is assumed, under certain assumption of betweenindividual design matrices. Similar inferential problems were also considered. The dental measurement data (see, e.g., Potthoff and Roy (1964, Biometrika 51, 313326)) was reexamined, based on extended growth curve models. (Fujikoshi, Kanda and Ohtaki, in press) 2) Some basic properties of the MLE's mu and SIGMA for a pvariate normal population Np (mu, SIGMA), based on a kstep monotone sample were studi
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ed. For k=2 and 3, we obtained the exact means and variances of mu and the exact bias of SIGMA.Asymptotic expansions of the distributions of these estimators were also obtained in the situation when the sample size is large. For a general k, the MLE's of mu and the usual transformed matrix DELTA of SIGMA were given in explicit forms. Some analogous properties were also obtained. (Kanda and Fujikoshi, 1998) 3) The problem whether there is an increasing timetrend of female proportion or not among 04 years old Japanese population in 19751994 was statistically considered. Based on national census data, the validity of the use of binomial model for analyzing female population number was examined using a betabinomial model. The increasing timetrend of female proportion was investigated by the means of testing the null hypothesis that female proportions are all equal against ordered alternatives. (Nakayama, Satoh and Ohtaki, submitted) 4) A method for making interval estimation of Relative Biological Effectiveness (RBE) with repeated measurements, based on growth curve analysis, was developed. Timedependent estimate of RBE can be obtained from our method. Using a set of data of mice experiments, we estimated the RBE of neutron ray on body weights after irradiation of neutron or gamma ray. (Satoh, Ohtaki et al., 1998) Less
