### 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 bootstrapping 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

Advanced Data Analysis from an Elementary Point of View

Posted by crshalizi at February 15, 2012 14:10 | permanent link