Ebook: Nonparametric Regression Analysis of Longitudinal Data

This monograph reviews some of the work that has been done for longitudi­ nal data in the rapidly expanding field of nonparametric regression. The aim is to give the reader an impression of the basic mathematical tools that have been applied, and also to provide intuition about the methods and applications. Applications to the analysis of longitudinal studies are emphasized to encourage the non-specialist and applied statistician to try these methods out. To facilitate this, FORTRAN programs are provided which carry out some of the procedures described in the text. The emphasis of most research work so far has been on the theoretical aspects of nonparametric regression. It is my hope that these techniques will gain a firm place in the repertoire of applied statisticians who realize the large potential for convincing applications and the need to use these techniques concurrently with parametric regression. This text evolved during a set of lectures given by the author at the Division of Statistics at the University of California, Davis in Fall 1986 and is based on the author's Habilitationsschrift submitted to the University of Marburg in Spring 1985 as well as on published and unpublished work. Completeness is not attempted, neither in the text nor in the references. The following persons have been particularly generous in sharing research or giving advice: Th. Gasser, P. Ihm, Y. P. Mack, V. Mammi tzsch, G . G. Roussas, U. Stadtmuller, W. Stute and R.

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This book is a research monograph in the relatively new field of nonparametric regression. It serves as an introduction to the field for graduate students, researchers and statistical consultants in statistics and biostatistics, but is also intended as an overview over some recent research developments in the fixed design case. Basic ideas are developed for various nonparametric curve estimators. The emphasis is on kernel estimators as a unifying concept and on the interplay between theory and practical application. Problems of practical application are illustrated in several examples of analyses of longitudinal medical data sets. These demonstrate the need of including nonparametric regression in addition to the classical parametric regression into the repertoire of practicing statisticians/biostatisticians. One goal of the book is to stimulate the reader to experiment with the methods and to gain experience by applying them. This is facilitated by an Appendix containing several relevant FORTRAN programs.

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This book is a research monograph in the relatively new field of nonparametric regression. It serves as an introduction to the field for graduate students, researchers and statistical consultants in statistics and biostatistics, but is also intended as an overview over some recent research developments in the fixed design case. Basic ideas are developed for various nonparametric curve estimators. The emphasis is on kernel estimators as a unifying concept and on the interplay between theory and practical application. Problems of practical application are illustrated in several examples of analyses of longitudinal medical data sets. These demonstrate the need of including nonparametric regression in addition to the classical parametric regression into the repertoire of practicing statisticians/biostatisticians. One goal of the book is to stimulate the reader to experiment with the methods and to gain experience by applying them. This is facilitated by an Appendix containing several relevant FORTRAN programs.
Content:
Front Matter....Pages I-VI
Introduction....Pages 1-5
Longitudinal Data and Regression Models....Pages 6-14
Nonparametric Regression Methods....Pages 15-25
Kernel and Local Weighted Least Squares Methods....Pages 26-46
Optimization of Kernel and Weighted Local Regression Methods....Pages 47-76
Multivariate Kernel Estimators....Pages 77-90
Choice of Global and Local Bandwidths....Pages 91-121
Longitudinal Parameters....Pages 122-130
Nonparametric Estimation of the Human Height Growth Curve....Pages 131-150
Further Applications....Pages 151-157
Consistency Properties of Moving Weighted Averages....Pages 158-164
Fortran Routines for Kernel Smoothing and Differentiation....Pages 165-189
Back Matter....Pages 190-199

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This book is a research monograph in the relatively new field of nonparametric regression. It serves as an introduction to the field for graduate students, researchers and statistical consultants in statistics and biostatistics, but is also intended as an overview over some recent research developments in the fixed design case. Basic ideas are developed for various nonparametric curve estimators. The emphasis is on kernel estimators as a unifying concept and on the interplay between theory and practical application. Problems of practical application are illustrated in several examples of analyses of longitudinal medical data sets. These demonstrate the need of including nonparametric regression in addition to the classical parametric regression into the repertoire of practicing statisticians/biostatisticians. One goal of the book is to stimulate the reader to experiment with the methods and to gain experience by applying them. This is facilitated by an Appendix containing several relevant FORTRAN programs.
Content:
Front Matter....Pages I-VI
Introduction....Pages 1-5
Longitudinal Data and Regression Models....Pages 6-14
Nonparametric Regression Methods....Pages 15-25
Kernel and Local Weighted Least Squares Methods....Pages 26-46
Optimization of Kernel and Weighted Local Regression Methods....Pages 47-76
Multivariate Kernel Estimators....Pages 77-90
Choice of Global and Local Bandwidths....Pages 91-121
Longitudinal Parameters....Pages 122-130
Nonparametric Estimation of the Human Height Growth Curve....Pages 131-150
Further Applications....Pages 151-157
Consistency Properties of Moving Weighted Averages....Pages 158-164
Fortran Routines for Kernel Smoothing and Differentiation....Pages 165-189
Back Matter....Pages 190-199
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