Nonparametric and Semiparametric Methods for Longitudinal Data Analysis

纵向数据涉及随时间重复观察的变量，在生物医学、流行病学、经济学、社会学等许多领域都很常见。非参数和半参数统计方法为从这类数据中提取有用的信息提供了有效的工具。这些方法使科学家、决策者和研究人员能够从数据中得出结论，而不依赖于可能对其环境限制太大的预先设定的假设。本建议的目的是发展系统的、理论上有充分根据的和更有效的这种方法。重点是以下五个专题：㈠进一步从理论和方法上发展时变系数模型的样条方法; ㈡估计协方差结构; ㈢将时变系数模型扩展为广义线性模型; ㈣扩展时变系数模型，以考虑累积协变量效应;（v）部分线性模型的半参数有效估计。这些项目涉及开发新的估计和推理程序，提供理论依据，并讨论其理论和实践的重要性，以生物医学和统计科学的进步。研究方法将是理论渐近分析，蒙特卡罗模拟和真实的数据分析相结合。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.