Mathematical Sciences: On the Construction of Efficient Estimates in Semi-Parametric and Nonparametric Models

一个一般的抽象理论已经发展为 构造感兴趣参数的有效估计 在半参数模型中，当数据独立且 相同分布。 本项目将在 两个方向。 一是发展满意 构造有效影响力的微积分 功能 二是对依附理论的拓展 数据 这项研究将提供一个统一的观点和一个严格的 构造大类估计量的数学基础 统计模型。 当模型仅部分指定时 就决定性特征或属性而言， 可以对新观测的预期行为进行建模 尽管如此，使用所谓的半参数或非参数 模型 这项工作做得有多好取决于 数据中的信息被利用，以及 模型可以用给定的数据来表示。 本研究着重于 抽象出必要的数学性质， 对未来观测的估计和良好预测。 则 这些所需性质的数学要求可以 推导

A general abstract theory has been developed for the construction of efficient estimates of the parameter of interest in semiparametric models when the data are independently and identically distributed. This project will expand this theory in two directions. First is the development of a satisfactory calculus for the construction of the efficient influence function. Second is the extension of the theory for dependent data. This research will provide a unified view and a rigorous mathematical basis for constructing estimators for a large class of statistical models. When models are only partially specified in terms of the determining features or attributes, the anticipated behavior for new observations can be modeled nonetheless using so-called semiparametric or nonparametric models. How well this is done depends on how fully the information in the data is utilized and on how precisely the model can be expressed given the data. This research focuses on abstracting the necessary mathematical properties for good estimates and good predictions for future observations. Then the mathematical requirements for these desired properties can be derived.