Collaborative Research: FRG: New development on nonparametric modeling and inferences with biological applications

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The objectives of this proposal are to develop new and widely applicablesemiparametric and nonparametric approaches to solve challengingstatistical problems from computational biology. Frontiers of biologicalresearch such as normalization and analysis of microarray and proteomicdata, functional connectivity of brains, covariate effects on longitudinaland functional data, and prediction of individual response trajectorieshave generated a number of outstanding statistical challenges. Severalnew semiparametric and nonparametric models have been introduced toaddress the imminent needs for the aforementioned biological applications. A number of innovative methods on nonparametric estimation and inferencesare proposed. Their properties will be investigated via both asymptotictheory and simulations. Their efficacy in biological applications will becarefully scrutinized. This proposal not only introduces a number ofinnovative techniques and useful statistical models, but also providesvarious new insights into nonparametric inferences. The research findingswill have significant impact on the future development of statisticaltheories and methodologies.Technological invention and information advancement have revolutionizedscientific research and technological development. Quantitative methodshave been widely employed in scientific communities. They have playedpivotal roles in knowledge discovery. This proposal intends to developnew nonparametric techniques and theories that arise from frontiers ofscientific development. In particular, the investigators will developmodels and cutting-edge technologies for the analysis of microarray,proteomic, longitudinal and functional data and fMRI brain images. Commoncharacteristics of these data are their complexity and size, wherenonparametric techniques are particularly powerful and under developed.The proposed techniques address imminent needs in computational aspects ofmolecular biology, neurology, and epidemiology. In addition, they willintegrate new mathematical developments with those in science andengineering, which empowers new knowledge discoveries and prudent policymaking. Undergraduate and graduate students, postdoctors andunderrepresented groups will be trained as results of this research.