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)回顾了无观察到不良反应水平的确定方法：基于Yanagawa等人(1994,1997)和Kikuchi等人(1993)提出的基于Akaike信息准则(AIC，Akaike 1973)的NOAEL方法，以克服传统方法使用统计检验的批评。(2)上述方法基于AIC模型选择的思想，预先假定参数的顺序限制。在阶数限制的假设下，偏差校正项是未知的，因此我们考虑用Bootstrap方法来估计偏差校正项。本研究认为Bootstrap方法在序限制的假设下会产生偏差。(3)在本研究的同时，我们从理论和应用两个方面考虑了用于不完全数据估计的EM算法。理论上，在Wu(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，我们考虑隐马尔可夫(HM)模型。我们从两个方面对HM模型进行了扩展。一种是引入自回归结构，另一种是具有二阶马尔可夫过程。具有自回归结构的模型在较宽的数据范围内变得比原始的HM模型和二阶模型更好地拟合。(5)研究了基于观测信息矩阵的方差估计不可能的情况下，EM算法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.