Simultaneous likelihood-based bootstrap confidence sets for a large number of models

Mayya Zhilova

No 2015-031, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics, and for adjusting the confidence level for multiplicity. Theoretical results state the bootstrap validity in the following setting: the sample size n is fixed, the maximal parameter dimension p_max and the number of considered parametric models K are s.t. (log?K )^12 p_max^3/n is small. We also consider the situation when the parametric models are misspecified. If the models' misspecification is significant, then the bootstrap critical values exceed the true ones and the simultaneous bootstrap confidence set becomes conservative. Numerical experiments for local constant and local quadratic regressions illustrate the theoretical results.

Keywords: simultaneous inference; correction for multiplicity; family-wise error; misspecified model; multiplier/weighted bootstrap GARCH; identification via heteroskedasticity (search for similar items in EconPapers)
JEL-codes: C13 C15 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb649:sfb649dp2015-031

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