The research will be directed toward the broad theme of recovering statistical information about variation of interest in the presence of confounding variation in high dimensions. The initial work involves developing new tools for the methodology of Generalized Estimating Equations (GEE) based on two new ideas: first, the investigator will develop a maximum information approach to the estimation of nuisance correlation parameters in GEE, and second, he will develop a quadratic inference methodology as an alternative to the point estimator/standard error approach. The first enhancement has been found to increase efficiency under covariance misspecification. The second allows one to develop ANOVA like model selection techniques for the estimating equation framework while automatically meeting the maximum information criterion. These new tools will then be used in a wider range of challenging applications involving high dimensional correlated data. An additional theme of the research is the development of more widely consistent nonparametric estimators for situations in which maximum likelihood fails.
Modern statistics is faced with an explosion of increasing complex and sophisticated scientific data. One of the key features of such data is that it is high-dimensional. It is also characterized by having high degrees of interdependence between observations. The goal of the research is to enhance our ability to separate the effects of this interdependence from the features of the data that we are most interested in. The initial focus of this research is on a popular method of dealing with longitudinal data, an example of which would be response variables that are measured repeatedly over time on a group of patients. The structure of the interdependence of observations within a patient is then a nuisance feature which we must adapt to if we wish to learn how the response variables are affected by explanatory variables. New methods will be developed that are more efficient and reliable for this setting, and they will then be extended to other problems with correlated structures.
