Constructing estimators based on orthogonal components in a parametric model

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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.