Separate inference induced from the structure of a statistical model

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1) It becomes clear that a useful model in practical applications involves in more parameters (parameters of high-demensions) than it is previously believed. A low-dimensional parameter is unble to describe a practical situation. Here we should note that the crude MLE behaves unfavorably in estimating a high-dimensional parameter. My previous efforts went to modifying the MLE through the conditional MLE,the estimating equation.2) The present research aimed at introducing a new family of distributions named the ruled exponential distributions. Then analytical properties of the family and their applications were discussed. A simple estimating function is investigated in relation with a family of distributions.3) More explicitly, the MLE based on a separate likelihood, mainly in the ruled exponential family, was pursued. Further, the present research extended to an obvious application to the estimating function and also to a modification of the family.4) A challenging topic is to unify the generalized regression model and the Stein type estimator. The present approach looks promising. We are making efforts to contributing this important problem, though a bulk of difficulties arise.