We consider the problem of obtaining appropriate weights for
averaging approximate (misspecified) models for
improved estimation of an unknown conditional mean in the face of model
uncertainty in heteroskedastic error settings. We
propose a "jackknife model averaging" (JMA) estimator which selects
the weights by minimizing a cross-validation criterion. This criterion is
quadratic in the weights, so computation of the weights is a simple application
of quadratic programming. We show that our estimator is asymptotically optimal
in the sense of achieving the lowest possible expected squared error. Monte Carlo
simulations and an illustrative application show that JMA can achieve
significant efficiency gains over existing model selection and averaging
methods in the presence of heteroskedasticity.
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Some
of the above material is based upon work supported by the National Science
Foundation under Grants No. SES-9022176, SES-9120576,
SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions,
or recommendations expressed in this material are those of the author(s), and
do not necessarily reflect the views of the NSF.