### Testing Regression Specifications (Advanced Data Analysis from an Elementary Point of View)

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

Advanced Data Analysis from an Elementary Point of View

Posted at February 19, 2013 10:30 | permanent link