Testing Regression Specifications (Advanced Data Analysis from an Elementary Point of View)
Three-Toed Sloth 2013-03-18
Summary:
Non-parametric smoothers can be used to test parametric models. Forms of tests: differences in in-sample performance; differences in generalization performance; whether the parametric model's residuals have expectation zero everywhere. Constructing a test statistic based on in-sample performance. Using simulation from the parametric model to find the null distribution of the test statistic. An example where the parametric model is correctly specified, and one where it is not. Cautions on the interpretation of goodness-of-fit tests. Why use parametric models at all? Answers: speed of convergence when correctly specified; and the scientific interpretation of parameters, if the model actually comes from a scientific theory. Mis-specified parametric models can predict better, at small sample sizes, than either correctly-specified parametric models or non-parametric smoothers, because of their favorable bias-variance characteristics; an example.
Reading: Notes, chapter 10; R for in-class demos Cox and Donnelly, chapter 7 Optional reading: Spain et al., "Testing the Form of Theoretical Models by Relaxing Assumptions: Comparing Parametric and Nonparametric Models", ssrn/2164297