Parametric Regression

Abstract

This chapter gives an introduction to several types of regression: simple and multiple linear, as well as simple polynomial and nonlinear regression. In all cases we identify the regression function in a parametric family, thus the title of the chapter. We also address issues of robustness, and we illustrate these concepts with a parallel comparison of the least squares and the least absolute deviations regression methods. Even though we introduce regression from a data smoothing point of view, we interpret the results in terms of statistical models, and we derive the statistical inference and diagnostic tools provided by the theory behind these statistical models. The chapter ends with a thorough discussion of the parametric estimation of the term structure of interest rates based on the Nelson-Siegel and Swensson families. As before, we try to work from examples, introducing theoretical results as they become relevant to the discussions of the analyzes which are used as illustrations.