Nonparametric Regression Analysis of Longitudinal Data

Abstract

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 global bandwidth choice.- 7.7 Weak convergence of a local bandwidth process.- 7.8 Practical local bandwidth choice.- 8. Longitudinal parameters.- 8.1 Comparison of samples of curves.- 8.2 Definition of longitudinal parameters and consistency.- 8.3 Limit distributions.- 9. Nonparametric estimation of the human height growth curve.- 9.1 Introduction.- 9.2 Choice of kernels and bandwidths.- 9.3 Comparison of parametric and nonparametric regression.- 9.4 Estimation of growth velocity and acceleration.- 9.5 Longitudinal parameters for growth curves.- 9.6 Growth spurts.- 10. Further applications.- 10.1 Monitoring and prognosis based on longitudinal medical data.- 10.2 Estimation of heteroscedasticity and prediction intervals.- 10.3 Further developments.- 11. Consistency properties of moving weighted averages.- 11.1 Local weak consistency.- 11.2 Uniform consistency.- 12. FORTRAN routines for kernel smoothing and differentiation.- 12.1 Structure of main routines KESMO and KERN.- 12.2 Listing of programs.- References.

Locations

• Library Union Catalog of Bavaria, Berlin and Brandenburg (B3Kat Repository) - View - PDF
• Technometrics - View