### Testing Parametric Regression Models with Nonparametric Smoothers (Advanced Data Analysis from an Elementary Point of View)

Testing parametric model specifications against parametric imposes strong
assumptions about how we can be wrong, and so is often dubious. Non-parametric
smoothers can be used to test parametric models instead. 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.

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notes, incorporating R examples

Advanced Data Analysis from an Elementary Point of View

Posted at February 16, 2011 01:45 | permanent link