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

这项建议的目的是发展新的和广泛适用的半参数和非参数方法来解决来自计算生物学的具有挑战性的统计问题。生物研究的前沿领域，如微阵列和蛋白质组数据的标准化和分析、大脑的功能连通性、纵向和功能数据的协变量效应以及个体反应轨迹的预测，都产生了一些突出的统计学挑战。一些新的半参数和非参数模型已经被引入，以满足上述生物学应用的迫切需要。提出了一些非参数估计和推断的创新方法。我们将通过渐近理论和模拟来研究它们的性质。它们在生物应用中的有效性将受到仔细的审查。这一建议不仅引入了许多创新技术和有用的统计模型，而且为非参数推断提供了各种新的见解。这些研究成果将对统计理论和方法的未来发展产生重大影响。技术发明和信息进步使科学研究和技术发展发生了革命性的变化。定量方法在科学界得到了广泛的应用。他们在知识发现中发挥了关键作用。这项提议旨在开发新的非参数技术和理论，这些技术和理论产生于科学发展的前沿。特别是，研究人员将开发用于分析微阵列、蛋白质组、纵向和功能数据以及功能磁共振脑图像的模型和尖端技术。这些数据的共同特征是它们的复杂性和大小，而非参数技术尤其强大和不发达。所提出的技术解决了分子生物学、神经学和流行病学计算方面的迫切需求。此外，他们将把新的数学发展与科学和工程领域的发展结合起来，从而促进新的知识发现和谨慎的政策制定。作为这项研究的结果，本科生和研究生、博士后和代表不足的群体将接受培训。

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.