Author | Mรผller, Hans-Georg. author |
---|---|
Title | Nonparametric Regression Analysis of Longitudinal Data [electronic resource] / by Hans-Georg Mรผller |
Imprint | New York, NY : Springer New York, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3926-0 |
Descript | XIV, 369 p. online resource |
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