The objectives of this proposal are to develop new and widely applicable semiparametric and nonparametric approaches to solve challenging statistical problems from computational biology. Frontiers of biological research such as normalization and analysis of microarray and proteomic data, functional connectivity of brains, covariate effects on longitudinal and functional data, and prediction of individual response trajectories have generated a number of outstanding statistical challenges. Several new semiparametric and nonparametric models have been introduced to address the imminent needs for the aforementioned biological applications. A number of innovative methods on nonparametric estimation and inferences are proposed. Their properties will be investigated via both asymptotic theory and simulations. Their efficacy in biological applications will be carefully scrutinized. This proposal not only introduces a number of innovative techniques and useful statistical models, but also provides various new insights into nonparametric inferences. The research findings will have significant impact on the future development of statistical theories and methodologies.
Technological invention and information advancement have revolutionized scientific research and technological development. Quantitative methods have been widely employed in scientific communities. They have played pivotal roles in knowledge discovery. This proposal intends to develop new nonparametric techniques and theories that arise from frontiers of scientific development. In particular, the investigators will develop models and cutting-edge technologies for the analysis of microarray, proteomic, longitudinal and functional data and fMRI brain images. Common characteristics of these data are their complexity and size, where nonparametric techniques are particularly powerful and under developed. The proposed techniques address imminent needs in computational aspects of molecular biology, neurology, and epidemiology. In addition, they will integrate new mathematical developments with those in science and engineering, which empowers new knowledge discoveries and prudent policy making. Undergraduate and graduate students, postdoctors and underrepresented groups will be trained as results of this research.
