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)我们回顾了Yanagawa等人提出的基于Akaike信息标准（AIC，Akaike 1973）确定无明显不良反应水平（NOAEL）的方法。(1994，1997）和菊池（Kikuchi）等人（1993）克服了对使用统计检验的传统方法的批评。(2)上述方法通过使用AIC的模型选择思想来确定NOAEL，并预先假设对参数的顺序限制。在阶约束的假设下，偏差校正项是未知的，因此我们考虑用自助法估计该项。在本研究中，我们发现在阶数限制的假设下，自助法会产生偏差。(3)同时，本文对EM算法在不完全数据下的估计问题进行了理论和应用方面的研究。理论上指出，在吴（1983）的假设下，广义EM算法并不总是收敛于极大似然估计。(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。一种是具有自回归结构的模型，另一种是具有二阶马尔可夫过程的模型。具有自回归结构的模型在较宽的数据范围内比原HM模型和二阶模型拟合得更好。(5)我们开始研究EM-算法在基于观测信息矩阵的方差估计不可能的情况下所得到的估计的精度。

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.