CAREER: Semiparametric and Non-Parametric Models for Correlated Data

职业：相关数据的半参数和非参数模型摘要：本研究项目旨在发展复杂高维相关数据的统计理论和实用方法，其中模型的全参数似然函数难以确定或难以确定，部分数据信息不准确或缺失。PI和她的合作者将通过将相关结构扩展到存在高维干扰参数的模型中来开发有效和鲁棒的估计程序，并开发用于低计算强度的假设检验的推断函数。该五年计划的部分研究目标是：使用二次推断函数提供允许保持估计器一致性的污染集群的显式最大数量;如果缺失的响应是随机缺失的，则开发无偏和有效的测试函数，以及用于测试模型假设的推断函数;为了开发一种对计算要求相对较低的使用非参数回归样条的有效Esimulator，引入具有卡方性质的拟合优度检验来检验非参数回归中的系数是时变的还是时不变的;并且，在本发明中，发展半-细胞周期微阵列数据的非参数模型，以结合基因内的时间相关性和生物相关基因之间的相关性。这项研究将有在生物医学研究、计量经济学、环境研究、海洋学、社会科学和公共卫生等经常出现相关数据的领域中产生了重大影响和许多应用。概述的研究项目有助于解决统计科学中的基本问题，并将激发大量科学家的兴趣。它也使理论和方法之间的联系，在计量经济学，统计学和生物统计学。这项研究将有助于生物医学研究，帮助对抗艾滋病和癌症等威胁生命的疾病，并将有助于更准确地识别细胞周期调控基因。它将通过开发关于非参数方法和微阵列数据分析的新课程，将拟议研究领域的现有知识充分融入教育活动，促进本科生和研究生在半参数和非参数方法方面的学习和培训。此外，它将扩大机会，使来自不同学科的所有公民都能参与，包括代表性不足的少数民族和国际伙伴关系。

CAREER: Semiparametric and nonparametric models for correlated dataAbstract:This research project is aimed at developing statistical theory andpractical methodology for complex high dimensional correlated datawhere the full parametric likelihood function of the model is difficultto specify or intractable, and partial data information is not accurateor is missing. The PI and her collaborators will developefficient and robust estimation procedures by incorporatingcorrelation structures into the models where high dimensionalnuisance parameters are present, and develop inference functionsfor hypothesis testing with low computational intensity.Part of research goals for the 5-year plan are:to provide an explicit maximum number of contaminatedclusters allowed to maintain the consistency of the estimator usingquadratic inference functions; to develop unbiased and efficientestimating functions if missing responses are missing at random,and inference functions for testing the model assumption;to develop an efficient esimator using a nonparametric regressionspline with relatively low demand on computation, and introduce agoodness-of-fit test with a chi-squared property for testing whethercoefficients in nonparametric regression are time-varying or timeinvariant; and, to develop semi-nonparametric models for cell cyclemicroarray data to incorporate both temporal correlation within genesand correlation between biologically related genes.This research will have significant impact and many applications inbiomedical research, econometrics, environmental studies, oceanography,social science and public health where correlated data ariseoften. The outlined research projects help to tackle fundamentalquestions in statistical science and will stimulate interest from alarge group of scientists. It also makes connections betweentheory and methods developed in econometrics, statistics andbiostatistics. The proposed research will benefit biomedical researchto help combat life threatening diseases such as AIDS and cancer,and will make contributions to identifying cell cycle regulated genesmore accurately. It will integrate current states of knowledge ofproposed research areas substantially into educational activitiesthrough development ofnew courses on nonparametric methods and microarray data analysis.It will advance undergraduate and graduate students' learning andtraining in semiparametric and nonparametric methods. Furthermore,it will broaden opportunities and enable theparticipation of all citizens from various disciplines, includingunderrepresented minorities and international partnerships.