Nonparametric Regression Analysis of Longitudinal Data

作者：Randall L. Eubank, Hans‐Georg Müller, Hans‐Georg Müller · 发表于：Technometrics · 年份：1990 · DOI：10.2307/1268867 · 被引用次数：331 · 研究领域：Advanced Statistical Methods and Models、Statistical Methods and Inference、Statistical and numerical algorithms

1. Introduction.- 2. Longitudinal data and regression models.- 2.1 Longitudinal data.- 2.2 Regression models.- 2.3 Longitudinal growth curves.- 3. Nonparametric regression methods.- 3.1 Kernel estimates.- 3.2 Weighted local least squares estimates.- 3.3 Smoothing splines.- 3.4 Orthogonal series estimates.- 3.5 Discussion.- 3.6 Heart pacemaker study.- 4. Kernel and weighted local least squares methods.- 4.1 Mean Squared Error of kernel estimates for curves and derivatives.- 4.2 Asymptotic normality.- 4.3 Boundary effects and Integrated Mean Squared Error.- 4.4 Muscular activity as a function of force.- 4.5 Finite sample comparisons.- 4.6 Equivalence of weighted local regression and kernel estimators.- 5. Optimization of kernel and weighted local regression methods.- 5.1 Optimal designs.- 5.2 Choice of kernel functions.- 5.3 Minimum variance kernels.- 5.4 Optimal kernels.- 5.5 Finite evaluation of higher order kernels.- 5.6 Further criteria for kernels.- 5.7 A hierarchy of smooth optimum kernels.- 5.8 Smooth optimum boundary kernels.- 5.9 Choice of the order of kernels for estimating b? functions.- 6. Multivariate kernel estimators.- 6.1 Definiton and MSE/IMSE.- 6.2 Boundary effects and dimension problem.- 6.3 Rectangular designs and product kernels.- 7. Choice of global and local bandwidths.- 7.1 Overview.- 7.2 Pilot methods.- 7.3 Cross-validation and related methods.- 7.4 Bandwidth choice for derivatives.- 7.5 Confidence intervals for anthropokinetic data.- 7.6 Local versus g...