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.
