Study on Theory of Nonlinear Statistical Models and Its Applications

(1)本项目的目的是(A)由组长和各研究员共同学习非线性统计的理论和方法；(B)就非线性统计的主题召开会议，以便彼此之间以及与组外的研究人员进行讨论。在(A)上，负责人和调查人员研究了几个主题。其中许多发表在若干科学期刊上或在国内/国际会议上发表。他们的详细情况在书面报告中列出，一些精选的作品在本报告的参考文献中。在(B)上，我们开了七次会。我们会议的题目如下。第一次非线性统计模型及其应用会议。(2)。非线性统计模型及其应用第二次会议在大分召开。(3)广岛大学非线性问题与实验设计会议。(4)成蹊大学非参数、非线性模型与仿真学术会议。(5)多巴非线性统计模型与数据分析会议。(6)金泽大学非线性统计模型与计算机学术会议。(7)松山实验数据与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。其中一些是基于既定的结果，一些是基于未解决的问题。它们大多是计算机密集的方法，如神经网络、平滑参数的确定和样条回归分析的计算点、随机数的生成、生长曲线模型、医学统计非线性模型、统计图形等。

(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.