Kernel smoothing in MATLAB : theory and practice of Kernel smoothing - Horova, Ivana; Kolacek, Jan.; Zelinka, Jiri. (Singapore : World Scientific Pub. Co., 2012)
'Methods of kernel estimates represent one of the most effective nonparametric smoothing techniques. These methods are simple to understand and they possess very good statistical properties. This book provides a concise and comprehensive overview of statistical theory and in addition, emphasis is given to the implementation of presented methods in Matlab. All created programs are included in a special toolbox which is an integral part of the book. This toolbox contains many Matlab scripts useful for kernel smoothing of density, cumulative distribution function, regression function, hazard function, indices of quality and bivariate density. Specifically, methods for choosing a choice of the optimal bandwidth and a special procedure for simultaneous choice of the bandwidth, the kernel and its order are implemented. The toolbox is divided into six parts according to the chapters of the book. All scripts are included in a user interface and it is easy to manipulate with this interface. Each chapter of the book contains a detailed help for the related part of the toolbox too. This book is intended for newcomers to the field of smoothing techniques and would also be appropriate for a wide audience: advanced graduate, PhD students and researchers from both the statistical science and interface disciplines'--BOOK JACKET.
1. Introduction. 1.1. Kernels and their properties. 1.2. Use of MATLAB toolbox. 1.3. Complements -- 2. Univariate kernel density estimation. 2.1. Basic definition. 2.2. Statistical properties of the estimate. 2.3. Choosing the shape of the kernel. 2.4. Choosing the bandwidth. 2.5. Density derivative estimation. 2.6. Automatic procedure for simultaneous choice of the kernel, the bandwidth and the kernel order. 2.7. Boundary effects. 2.8. Simulations. 2.9. Application to real data. 2.10. Use of MATLAB toolbox. 2.11. Complements -- 3. Kernel estimation of a distribution function. 3.1. Basic definition. 3.2. Statistical properties of the estimate. 3.3. Choosing the bandwidth. 3.4. Boundary effects. 3.5. Application to data. 3.6. Simulations. 3.7. Application to real data. 3.8. Use of MATLAB toolbox. 3.9. Complements -- 4. Kernel estimation and reliability assessment. 4.1. Basic definition. 4.2. Estimation of ROC curves. 4.3. Summary indices based on the ROC curve. 4.4. Other indices of reliability assessment. 4.5. Application to real data. 4.6. Use of MATLAB toolbox -- 5. Kernel estimation of a hazard function. 5.1. Basic definition. 5.2. Statistical properties of the estimate. 5.3. Choosing the bandwidth. 5.4. Description of algorithm. 5.5. Application to real data. 5.6. Use of MATLAB toolbox. 5.7. Complements -- 6. Kernel estimation of a regression function. 6.1. Basic definition. 6.2. Statistical properties of the estimate. 6.3. Choosing the bandwidth. 6.4. Estimation of the derivative of the regression function. 6.5. Automatic procedure for simultaneous choice of the kernel, the bandwidth and the kernel order. 6.6. Boundary effects. 6.7. Simulations. 6.8. Application to real data. 6.9. Use of MATLAB toolbox. 6.10. Complements -- 7. Multivariate kernel density estimation. 7.1. Basic definition. 7.2. Statistical properties of the estimate. 7.3. Bandwidth matrix selection. 7.4. A special case for bandwidth selection. 7.5. Simulations. 7.6. Application to real data. 7.7. Use of MATLAB toolbox. 7.8. Complements.
Includes bibliographical references (p. 213-223) and index.
Keywords: Smoothing (Statistics); Kernel functions