U.S.-Australia Cooperative Research: Topics in Semiparametric Modeling

该奖项将支持博士之间的合作研究。 康奈尔大学的大卫鲁珀特和 澳大利亚国立大学.二进制问题 回归分析是将结果Y与预测因子相关联 X.这种问题的一个例子是将饮食和其他 个人因素（X）预测乳房发育 癌症（Y）。 通常这种二元回归问题是 通过逻辑回归关系建模。重点 本研究的主要内容是当X存在测量误差时， 替代W被用作X的估计。最近，mathe- 数学家研究了逻辑回归问题 预测器中的测量误差，并指出 忽略测量误差并执行 Y对W的普通逻辑回归导致不一致 这些参数的严重偏差估计 方程一种解决方案已被提出， 测量误差问题是一个半参数方法， 它依赖于原始的参数逻辑回归 模型结合非参数回归技术。 基于这一解决方案， 一个项目是研究几个普遍重要的问题 通过将经典参数与 更现代的非参数技术。理论问题 涉及非参数和参数分量的估计 将进行调查。参数和非参数的组合 解决二元回归问题的度量技术 当预测者受到测量误差的影响时， 研究了第三个研究领域将涉及合并数据 转换和非参数回归。 该项目代表了 美国数学家，其工作在国家科学下 基础支持，侧重于非参数回归 分析和澳大利亚小组，谁出版了许多 这一领域的开创性论文这是一个重要的基础 努力推进非参数技术的使用， 数理统计的重要问题。

This award will support collaborative research between Dr. David Ruppert of Cornell University and Dr. Peter Hall of the Australian National University. The problem of binary regression analysis is to relate an outcome Y to a predictor X. An example of such a problem is to relate diet and other personal factors (X) to predict the development of breast cancer (Y). Usually such binary regression problems are modeled through a logistic regression relationship. The focus of this research is on cases when X has measurement error and a surrogate W is used as an estimate of X. Recently, mathe- maticians have studied the problem of logistic regression with measurement error in predictors, and have pointed out that ignoring the measurement error and performing an ordinary logistic regression of Y on W leads to inconsistent and seriously biased estimates of the parameters in these equations. One solution which has been proposed to the problem of measurement error is a semiparametric method, which relies on the original parametric logistic regression model combined with nonparametric regression techniques. Building on this proposed solution, the objective of this project is to work on several problems of general importance to statistics through combining classical parametric with the more modern nonparametric techniques. Theoretical problems involving estimation of nonparametric and parametric components will be investigated. Combination of parametric and nonpara- metric techniques to solve the problem of binary regression when the predictors are subject to measurement error will be studied. A third study area will concern combining data transformation and nonparametric regression. The project represents excellent collaboration between the U.S. mathematician, whose work, under National Science Foundation support, focuses on nonparametric regression analysis and the Australian group, who have published many of the seminal papers in this area. This is important fundamental work in advancing the use of nonparametric techniques in important problems of mathematical statistics.