The proposal has four projects that involve the application of logspline methodology to survival analysis and stationary stochastic processes. The primary objective of the first project is to systematically extend survival analysis in all of its various aspects to handle multivariate data involving censored responses and covariates and to do so in a manner that will efficiently balance model bias and variance in the estimates. The second project considers the problem of estimating survival and hazard functions for bivariate censored failure times. Since this is a new and important research area in survival analysis, the project is further divided into two subprojects. The first considers the estimation of the bivariate survival function without covariates, and the second considers regression analysis involving covariates. The goal is to provide a consistent and unified nonparametric framework for bivariate survival analysis. In particular, asymptotic properties of the proposed procedures will be established. The third project considers the estimation of a possibly mixed spectral distribution of a stationary process. The objective is to establish asymptotic properties for the joint estimator of continuous and discrete spectra. Extensions to other stationary processes such as spatial and point processes will also be emphasized. The fourth project considers nonparametric time series regression. Its objective is to study the asymptotic properties of regression function estimates subject to having the form of a specified sum of functions of at most d variables. The first project in this proposal involves the development of several statistical procedures for identifying and evaluating important risk factors that are related to the occurrence and recurrence of various diseases such as coronary heart disease, breast, lung, prostate and colon cancers. The second project studies the effects of these risk factors on the relationship between causes of several diseases. Specifically, the method will be appl ied to study (1) the laser photocoagulation eye treatment for diabetic patients, (2) survival probabilities of nonfatal myocardial infarction and heart failures, (3) the relationship of recurrence and survival times of colon or breast cancer patients. The third project develops statistical procedures for studying elements of the nervous system and to understand how they function and work together. Through this developments, we hope to explain things such as memory, emotion, learning, sleep and expectation. The fourth project develops efficient prediction procedures for applications in environmental studies such as temperature effect on riverflow, ozone concentration.
