Martin Jullum: Parametric or Nonparametric: The Focused Information Criterion Approach

Martin Jullum (Department of Mathematics, UiO), gives a seminar in  Auditorium 4, Vilhelm Bjerknes house, at 14:15, Tuesday March 4th: 

Parametric or Nonparametric: The Focused Information Criterion Approach

Abstract:

A long-living question is whether one should rely on a parametric or nonparametric
model when analyzing a certain data set. This is a question that cannot be answered
by classical model selection criteria like AIC and BIC, since the nonparametric
model has no likelihood. In addition, comparison based on goodness of
fit measures has the drawback that one, somewhat artificially, has to choose
the test level. When performing a statistical analysis, there is often a certain
population quantity, here coined the focus parameter, which is of primary interest.
We develop a focused information criterion (FIC) for comparing general non-nested
parametric models with a nonparametric alternative. The FIC is a model selection
criterion which compares and ranks candidate models based on estimated precision
of the model estimators for the focus parameter. It has earlier been developed
for several classes of problems mainly involving parametric models. Including
the asymptotically unbiased nonparametric candidate model is beneficial as it ‘saves the day' when none of the parametric models perform well – while leaving estimation to the parametric models when they do perform well. In this talk, the derivation of the FIC
for ‘parametrics vs. nonparametrics’ will be sketched for the i.i.d. situation, and
the properties of this scheme will be illustrated. An extension to an averaged focused
information criterion (AFIC) will also be outlined. Certain special cases of the latter
criterion relate to the Cramér-von Mises and Pearson’s chi-squared test statistics,
where AFIC give asymptotic significance levels through theoretical justifications,
rather than by ‘tradition’. Other extension, for instance to survival analysis models,
will be discussed briefly.

 

Published Jan. 31, 2014 9:32 AM - Last modified June 13, 2014 11:40 AM