Development of Computer Software for Analyzing Growth Curve Date.

Fujikoshi和Satoh导出了平衡设计的扩展生长曲线模型下未知参数的最大似然估计，并研究了几种统计性质。他们开发了使用AIC和C的修正版本进行模型选择的新方法，并证明这些方法具有良好的小样本特性（Fujikoshi和Satoh， Hiroshima Mathematical J.26,1996, Biometrika in press， J.Multivariate Analysis, in press）。Kanda和Seo通过推广多元方差分析模型的原始方法，研究了具有正定、序列和均匀协方差结构的多重比较。他们使用改进的二阶近似程序给出了同时置信区间。他们还在协方差结构模型下推导了二元Hotelling T^2型变量联合概率的渐近展开式（J.Japan Statistical Society 26,1996）。Ohtaki与Satoh和Katou合作开发了一套计算机程序Growth2 (Ver.3.2)，该程序适用于不平衡设计的生长曲线数据。所使用的算法基于Vonesh&Carter（1984）的理论扩展版本的结果，在估计过程中不需要任何迭代，适用于平均参数存在线性限制的情况。在编程中，使用Fortran77和Pascal进行数值处理，并使用Delphi （Ver.2.0J）构建图形用户界面，提高了程序的可操作性（Proc.of the Research Institute for Radiation Biology and Medicine 37,1996）。

Fujikoshi and Satoh derived the maximum likelihood estimates of unknown parameters under the extended growth curve model with a balanced design, and studied the several statistical properties. They developed new methods for model selection with corrected versions of AIC and C,and proved that those methods have good small sample properties (Fujikoshi and Satoh, Hiroshima Mathematical J.26,1996, Biometrika in press, J.Multivariate Analysis, in press).Kanda and Seo studied a multiple comparison by original of generalizing the Multivariate Analysis of Variance model with, a positive definite, serial, and uniform covariance structures. They gave the simultaneous confidence intervals using modified second approximation procedure. They also derived the asymptotic expansions for the joint probability of bivariate Hotelling T^2-type variates under the model with the covariance structures (J.Japan Statistical Society 26,1996).Cooperating with Satoh and Katou, Ohtaki developed a package of computer programs referred to as Growth2 (Ver.3.2) which is applicable to the growth curve data with the unbalanced design. The algorithm used is based on the result of expanded version of the theory due to Vonesh&Carter (1984) which needs not any iteration in the estimating procedure, and is applicable to the cases where linear restriction exists in the mean parameters. In the programming, Fortran77 and Pascal were used for a numeric processing, and Delphi (Ver.2.0J) was also used for constructing the graphic user interface, which improves the operativeness of the program (Proc.of the Research Institute for Radiation Biology and Medicine 37,1996).