Statistical Determination of the No-Observed-Adverse-Effect Levels based on the Information Criteiron under Order Restriction

研究结果总结如下。(1)回顾了确定未观察到的不良影响水平的方法；NOAEL，基于Yanagawa等人（1994,1997）和Kikuchi等人（1993）提出的赤池信息标准（AIC, Akaike 1973），以克服使用统计检验的传统方法的批评。(2)上述方法采用AIC模型选择的思想确定NOAEL，并预先假设参数的顺序限制。在阶数限制的假设下，偏置校正项是未知的，因此我们考虑用自举法估计偏置校正项。本研究表明，在序约束的假设下，自举法会产生偏差。(3)在研究的同时，我们从理论和应用两个方面考虑了基于不完整数据估计的em算法。从理论上表明，在Wu（1983）给出的假设下，广义em -算法并不总是收敛到最大似然估计。(4)作为em算法的一个应用方面，我们考虑了隐马尔可夫（HM）模型。我们从两个方面扩展了HM模型。一种是自回归结构，另一种是二阶马尔可夫过程。具有自回归结构的模型对大范围数据的拟合优于原HM模型和二阶模型。(5)当无法根据观测到的信息矩阵估计方差时，我们开始研究em算法估计的准确性。

The summary of research results is as follows.(1) We review the method to determine the No-Observed-Adverse-Effect Levels ; NOAEL, based on Akaike Information Criterion (AIC, Akaike 1973), which was proposed by Yanagawa et al.(1994, 1997) and Kikuchi et al.(1993) to overcome the criticism of the conventional method using statistical tests.(2) The above method determines the NOAEL by the idea of model selection using AIC, assuming the order restriction on the parameters in advance. Bias correction term is unknown under the assumption of order restriction, so we consider the estimation of this term using the bootstrap method. It is suggested in this research that the bootstrap method yields a bias under the assumption of order restriction.(3) Concurrently with this study, we consider EM-algorithm which is used to the estimation based on the incomplete data, both in theoretical and applicative aspects. Theoretically, it is indicated that the generalized EM-Algorithm does not always converges to the maximum likelihood estimate under tha assumption given by Wu (1983).(4) As an applicative aspect of EM-algorithm, we consider hidden Markov (HM) model. We extend HM model in two ways. One is that incorporated an autoregressive structure and the other has the second order Markov process. The model with the autoregressive structure becomes to fit better than original HM model and the second order model for the wide range of data.(5) We start to study on the accuracy of the estimates obtained by EM-algorithm when the estimation of the varince based on the observed information matrix is impossible.