Constructing estimators based on orthogonal components in a parametric model

在参数估计的关系中，提出了参数分量间正交性的概念。有希望的情况是：1)参数维数高；2)分布函数参数化良好。这些限制听起来可能很严格，但在实践中可以在此限制下构建灵活的模型。在许多有趣的问题中，目前的研究主要集中在两个主题上；高维平均参数的同时估计和回归模型，重点是对数连接函数。成功地获得了与前一个主题有关的几个结果。此外，与贝叶斯方法的密切关系也引起了我们的注意。这一发现将对我们后续的研究有很大的帮助。具体结果涉及1)两个估计方程的意外应用（将出现在SPL中），2)有序微分方程的应用（将出现在CIS中），3)正交性概念（手稿）和对偶共轭先验（准备中）。除最后一篇稿件外，其余三篇稿件均收录在本研究报告中。虽然我们获得了一些关于后一个主题的回归模型的结果。结果还没有达到令人满意的水平。本学科显然与统计学理论和应用中最具吸引力的学科有关。所有常用的方法，如方程估计法、平滑法和分离推理法，都希望能有效地利用正交性的概念。希望本文的研究对加强这一领域的研究有所贡献。

The notion of orthogonality among components of a parameter is developed in relation with the estimation of the parameter. The promising situation are : 1) The dimension of a parameter high and 2) Distribution functions are parameterized in a favorable way. These restrictions may sound severely restrictive, but flexible models can be constructed in practice under this restriction.Among many interesting problems the present research focused on the two subjects ; the simultaneous estimation of a high-dimensional mean parameter and the regression model with emphasis on the logarithmic link function. Several results relating the former subject were successfully obtained. In addition, a close relation with Bayesian approach has been called our attention. This finding will be significantly benefited for our subsequent researches. Specific results are concerned with 1) an unexpected application of the two estimating equation (to be appeared in SPL), 2) an application of the ordinal differential equation (to be appeared in CIS), 3) notions of orthogonality (Manuscript) and dual conjugate prior (in preparation). The three manuscripts except for the last are filed in the report of this research. Although we obtained some results on the latter subject of the regression model. The results are still below the satisfactory level.The present subject is obviously related with the most attractive subjects in both the theory and application of statistics. All the enthusiastic methods such as estimating equations, smoothing methods and separate inference are expected to owe the efficient use of the notion of orthogonality. It is my hope that the present research made a significant contribution on enhancing the research in this line.