Smoothing Techniques With Implementation in S [Paperback]

The author has attempted to present a book that provides a non-technical introduction into the area of non-parametric density and regression function estimation. The application of these methods is discussed in terms of the S computing environment. Smoothing in high dimensions faces the problem of data sparseness. A principal feature of smoothing, the averaging of data points in a prescribed neighborhood, is not really practicable in dimensions greater than three if we have just one hundred data points. Additive models provide a way out of this dilemma; but, for their interactiveness and recursiveness, they require highly effective algorithms. For this purpose, the method of WARPing (Weighted Averaging using Rounded Points) is described in great detail.The author has attempted to present a book that provides a non-technical introduction into the area of non-parametric density and regression function estimation. The application of these methods is discussed in terms of the S computing environment. Smoothing in high dimensions faces the problem of data sparseness. A principal feature of smoothing, the averaging of data points in a prescribed neighborhood, is not really practicable in dimensions greater than three if we have just one hundred data points. Additive models provide a way out of this dilemma; but, for their interactiveness and recursiveness, they require highly effective algorithms. For this purpose, the method of WARPing (Weighted Averaging using Rounded Points) is described in great detail.I. Density Smoothing.- 1. The Histogram.- 1.0 Introduction.- 1.1 Definitions of the Histogram.- The Histogram as a Frequency Counting Curve.- The Histogram as a Maximum Likelihood Estimate.- Varying the Binwidth.- 1.2 Statistics of the Histogram.- 1.3 The Histogram in S.- 1.4 Smoothing the Histogram by WARPing.- WARPing Algorithm.- WARPing in S.- Exercises.- 2. Kernel Density Estimation.- 2.0 Introduction.- 2.1 Definition of the Kernel Estimate.- Varying the Kernel.- Val3–