| KUNIO TAKEZAWA, PhD, is a Specific Research Scientist in the Department of Information Science and Technology at the National Agricultural Research Center, Japan. He is also an Associate Professor in the Cooperative Graduate School System at the Graduate School of Life and Environmental Sciences at the University of Tsukuba, Japan. Dr. Takezawa holds several patents in mathematics and is the recipient of a Research Award from the Japan Science and Technology Agency and a Thesis Award from the Japanese Agricultural Systems Society. |
| Preface Acknowledgments 1 Exordium 1.1 Introduction 1.2 Are the moving average and Fourier series sufficiently useful? 1.3 Is a histogram or normal distribution sufficiently powerful? 1.4 Is interpolation sufficiently powerful? 1.5 Should we use a descriptive equation? 1.6 Parametric regression and nonparametric regression 2 Smoothing for data with an equispaced predictor 2.1 Introduction 2.2 Moving average and binomial filter 2.3 Hat matrix 2.4 Local linear regression 2.5 Smoothing spline 2.6 Analysis on eigenvalue of hat matrix 2.7 Examples of S-Plus object References Problems 3 Nonparametric regression for one-dimensional predictor 3.1 Introduction 3.2 Trade-off between bias and variance 3.3 Index to select beneficial regression equations 3.4 Nadaraya-Watson estimator 3.5 Local polynomial regression 3.6 Natural spline and smoothing spline 3.7 LOESS 3.8 Supersmoother 3.9 LOWESS 3.10 Examples of S-Plus object References Problems 4 Multidimensional smoothing 4.1 Introduction 4.2 Local polynomial regression for multidimensional predictor 4.3 Thin plate smoothing splines 4.4 LOESS and LOWESS with plural predictors 4.5 Kriging 4.6 Additive model 4.7 ACE 4.8 Projection pursuit regression 4.9 Examples of S-P/us object References Problems 5 Nonparametric regression with predictors represented as distributions 5.1 Introduction 5.2 Use of distributions as predictors 5.3 Nonparametric DVR method 5.4 Form of nonparametric regression with predictors represented as distributions 5.5 Examples of S-Plus object References Problems 6 Smoothing of histograms and nonparametric probability density functions 7.Pattern Recognition. Appendix A: Creation and Applications of B-Spline Bases. Appendix B: R Objects. Appendix C: Further Readings. Index. |
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