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19 Result(s)
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Hans-Georg Müller
Mathematics
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Article
Quantifying functionals of age distributions in the wild by solving an operator equation
Residual demography is a recent concept that has proved to be a useful tool to gain insights about the age distributions of wild populations, especially insects. We develop an operator equation that permits th...
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Article
Surface and function approximation with nonparametric regression
Several methods are considered for the reconstruction of smooth functions and surfaces from noisy measurements. These methods are statistically motivated and belong to the area of nonparametric regression. The...
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Chapter
Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation
We give an overview on applications of weak convergence of stochastic processes to obtain adaptive nonparametric curve estimators through efficient data-based local bandwidth choices. We point out new developm...
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Article
Locally adaptive hazard smoothing
We consider nonparametric estimation of hazard functions and their derivatives under random censorship, based on kernel smoothing of the Nelson (1972) estimator. One critically important ingredient for smoothi...
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Book
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Chapter
Introduction
If we analyse longitudinal data, we are usually interested in the estimation of the underlying curve which produces the observed measurements. This curve describes the time course of some measured quantity lik...
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Chapter
Further Applications
The remarks made here concern typical problems in the medical field which can as well be encountered in other fields of application. Longitudinal medical data are not only collected with the aim of description...
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Chapter
Nonparametric Regression Methods
Besides kernel estimators, commonly used nonparametric regression estimators are local least squares estimators and smoothing splines. Besides these estimators, we also discuss orthogonal series estimators whi...
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Chapter
Fortran Routines for Kernel Smoothing and Differentiation
The programs listed below are suited for kernel estimation and differentiation (υ=0–3) with estimators (4.4); various kernels of different orders can be chosen and there are two options for bandwidth choices: ...
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Chapter
Nonparametric Estimation of the Human Height Growth Curve
As an example of an application of some of the methods discussed before, the analysis of the human height growth curve by nonparametric regression methods is considered. The data that are analysed were obtaine...
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Chapter
Longitudinal Data and Regression Models
There exist several kinds of longitudinal data, i.e., measurements (observations) of the same quantity (occurrence) on the same subject at different time points, each of which requires different methods for an...
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Chapter
Consistency Properties of Moving Weighted Averages
We consider here the usual fixed design regression model $$ Y_{i,n} {\text{ = g(t}}_{i,n} ) + \varepsilon _{i,n} $$ with tri...
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Chapter
Kernel and Local Weighted Least Squares Methods
It is assumed from now on that in the model (2.1) $$ {\text{Y}}_i {\text{,n-g(t}}_{i,n} ) + \varepsilon _{i,n} {\text{ ,i = 1,}}...{\text{,n}}...
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Chapter
Multivariate Kernel Estimators
The kernel estimate (4.4) can be generalized to the case of a multivariate regression function g: A → ℝ where A ⊂ ℝm, m ≥ 1. The proofs usually can be generalized from the univariate case without difficulty. Ther...
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Chapter
Longitudinal Parameters
In biomedical settings, a common problem is the comparison and description of samples of curves. Assuming there are N subjects and nj measurements are made for the j-th subject, we might describe the situation by...
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Chapter
Optimization of Kernel and Weighted Local Regression Methods
Optimization here means minimization of the asymptotically leading term of the IMSE. Since the asymptotic expression for the IMSE is the same for both kernel and weighted local least squares methods, optimizat...
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Chapter
Choice of Global and Local Bandwidths
For practice applications of curve smoothing methods, the choice of a good smoothing parameter is a very important issue. For kernel and weighted local least squares estimators this is the choice of the bandwi...
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Chapter and Conference Paper
Optimal convergence properties of kernel estimates of derivatives of a density function
We consider kernel estimates for the derivatives of a probability density which satisfies certain smoothness conditions. We derive the rate of convergence of the local and of the integrated mean square error (...
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Chapter and Conference Paper
Kernel estimation of regression functions
For the nonparametric estimation of regression functions with a one-dimensional design parameter, a new kernel estimate is defined and shown to be superior to the one introduced by Priestley and Chao (1972). T...
