Nonparametric Statistical Methods, 3rd Edition

Chapter 14

Smoothing

Introduction

The wavelet methods from Chapter 13 are useful at estimating a function from a sample of bivariate data because these methods do not rely on specific assumptions about the functional relation underlying the data. In contrast, the functional estimation problems considered in Chapters 9 and 11 were designed to estimate very specific types of functions. In this chapter, we continue to pursue methods to estimate a general function from a collection of bivariate observations.

Wavelet methods projected the data into resolution levels at various scales (frequencies) through the use of a set of special basis functions. The properties of wavelets lead to representing the data by a greatly reduced set of objects through the nonlinear process of thresholding. The methods presented here are “smoothers.” Similar to wavelet methods, these smoothers may make use of external functions to model the functional relation between and . These functions, however, neither form a basis for a space of functions nor do they provide a dimension reduction property or analyze an observed function in terms of scale and location. Additionally, the external functions used in smoothers ...