Mathematical Sciences: Exploring Regression Structure Using Nonparamentric Functional Estimation

本研究致力于对形式选择的研究 统计回归函数的外生 当外生变量的数量为 大.通常的做法是施加条件，例如 线性或可加性，以避免与 高维稀疏数据。平均导数的估计 函数将用于选择或拒绝特定的 对回归形式的限制。泛函 被认为是积分型，这可能允许他们的估计 以通常的参数速率。这些泛函的估计 这是基于核密度估计将被认为是 并分析了它们的大样本性质。这些评估人员将 然后用它来测试各种关于形式的假设， 回归函数。的有限样本行为 建议的估计和测试将研究使用构造 和真实的数据。在某些条件下，这些估计量将 研究了它们在识别投影方向中的用途， 投影寻踪回归相似泛函 类似于Fisher信息矩阵， 确定投影寻踪密度估计中的方向。

This research is devoted to the study of choice of the form of the statistical regression function in terms of the exogenous variables in the model when the number of exogenous variables is large. The common practice is to impose conditions such as linearity or additivity to avoid the difficulties associated with sparse data in high dimensions. Estimates of average derivative functionals will be used to select or reject a particular restriction on the form of the regression. The functionals considered are of integral type which may allow their estimation at the usual parametric rate. Estimators of these functionals which are based on kernel density estimators will be considered and their large sample properties analyzed. These estimators will then be used to test various hypotheses concerning the form of the regression function. The finite sample behavior of the proposed estimators and tests will be studied using constructed and real data. Under certain conditions these estimators will be studied for their use in identifying projection directions in projection pursuit regression. Similar functionals closely resembling the Fisher information matrix will be used to determine directions in projection pursuit density estimation.