Nonparametric and Semiparametric Methods for Longitudinal Data Analysis

摘要DMS-0204556PI：建华黄埔纵向数据是生物医学、流行病学、经济学、社会学等诸多领域中普遍存在的一种数据，它涉及到随时间重复观测的变量。非参数和半参数统计方法为从这类数据中提取有用信息提供了有效的工具。这些方法允许科学家、政策制定者和研究人员从他们的数据中得出结论，而不需要依赖于预先指定的假设，这些假设可能对他们的设置过于严格。这项建议的目标是开发系统的、理论上有充分依据的、更有效的这种方法。重点讨论了以下五个问题：(I)基于样条法的时变系数模型的理论和方法的进一步发展；(Ii)协方差结构的估计；(Iii)将时变系数模型推广到广义线性模型；(Iv)考虑累积协变量影响的时变系数模型的推广；(V)部分线性模型中的半参数有效估计。这些项目包括开发新的估计和推理程序，提供理论依据，并讨论它们对促进生物医学和统计科学发展的理论和实践意义。研究方法将是理论渐近分析、蒙特卡罗模拟和实际数据分析相结合。将使用带样条函数的全局平滑技术。

AbstractDMS-0204556PI: Jianhua HuangLongitudinal data, which involve variables observed repeatedly over time, are common in biomedicine, epidemiology, economics, sociology, and many other fields. Nonparametric and semiparametric statistical methods provide effective tools for extracting useful information from this type of data. These methods allow scientists, policy makers and researchers to draw conclusions from their data without depending on pre-specified assumptions that may be too restrictive to their settings. The objective of this proposal is to develop systematic, theoretically well-founded, and more efficient such methods. The focus is on the following five topics: (i) further theoretical and methodological development of the spline-based approach to time-varying coefficient models; (ii) estimation of covariance structures; (iii) extension of time-varying coefficient models to generalized linear models; (iv) extension of time-varying coefficient models to take into account accumulative covariate effects; (v) semiparametric efficient estimation in partly linear models. These projects involve developing novel estimation and inference procedures, providing theoretical justification, and discussing their theoretical and practical importance to the advancement of biomedical and statistical science. The research approach will be a combination of theoretical asymptotic analysis, Monte Carlo simulations and real data analysis. Global smoothing techniques with spline functions will be used.