Study on Theory of Nonlinear Statistical Models and Its Applications

（一）.本项目的目的是（A）由首席研究员和研究员研究非线性统计的理论和方法，（B）就非线性统计的主题举行会议，以便相互讨论并与本小组以外的研究人员进行讨论。（二）、在（A）中，负责人和调查人员研究了几个主题。其中许多已在若干科学期刊上发表或在国内/国际会议上提出。这些研究成果的详细情况已在书面报告中列出，部分选编作品作为本报告的参考文献。（三）、在（B），我们举行了七次会议。我们会议的标题如下。（一）.第一次非线性统计模型及其应用会议。（二）、第二次非线性统计模型及其应用会议。(3)广岛大学非线性问题与实验设计会议。(4)在成蹊大学举行的非参数、非线性模型和模拟会议。(5)在多巴举行的非线性统计模型和数据分析会议。(6)金泽大学非线性统计模型与计算机会议。(7)在松山举行的实验数据和非线性统计模型会议。这些会议的主题从理论统计到具有非线性结构的实际数据的分析。其中一些是关于既定的结果，一些是关于未解决的问题。这些方法大多是计算机密集型方法，如神经网络、样条回归分析中光滑参数和计算点的确定、随机数的产生、生长曲线模型、医学统计中的非线性模型、统计图形学等。

(1). The objects of this project are (A) to study theory and methods on nonlinear statistics by the head investigator and the investigators and (B) to hold meetings on topics of nonlinear statistics in order to have discussion with each other and with researchers outside our group.(2). On (A), the head and the investigators studied several topics. Many of them are published in several scientific journals or presented at domestic/international meetings. The details of them are listed in the written report and some selected works are at references of this report.(3). On (B), we held meetings seven times. The titles of our meetings are as followes.(1). First meeting on nonlinear statistical models and its applications at Kure.(2). Second meeting on nonlinear statistical models and its applications at Oita.(3) Meeting on nonlinear problem and experimental design at Hiroshima University.(4) Meeting on nonparametrics, nonlinear models and simulation at Seikei University.(5) Meeting on nonlinear statistical models and data analysis at Toba.(6) Meeting on nonlinear statistical models and computer at Kanazawa University.(7) Meeting on experiment data and nonlinear statistical models at Matsuyama.The topics presented at these meetings are from theoretical statistics to analysis of practical data having nonlinear structure. Some of them are on established results and some are on unsolved problems. Most of them are on computer intensive methods such as neural networks, determination of smoothing parameter and computation points on spline regression analysis, generation of random numbers, growth curve model, nonlinear models at medical statistics, statistical graphics and so on.