Degenerate <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$U$$</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$V$$</EquationSource> </InlineEquation>-statistics under ergodicity: asymptotics, bootstrap and applications in statistics
We derive the asymptotic distributions of degenerate <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$U$$</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$$V$$</EquationSource> </InlineEquation>-statistics of stationary and ergodic random variables. Statistics of these types naturally appear as approximations of test statistics. Since the limit variables are of complicated structure, typically depending on unknown parameters, quantiles can hardly be obtained directly. Therefore, we prove a general result on the consistency of model-based bootstrap methods for <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$$U$$</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$$V$$</EquationSource> </InlineEquation>-statistics under easily verifiable conditions. Three applications to hypothesis testing are presented. Finally, the finite sample behavior of the bootstrap-based tests is illustrated by a simulation study. Copyright The Institute of Statistical Mathematics, Tokyo 2013
Year of publication: |
2013
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Authors: | Leucht, Anne ; Neumann, Michael |
Published in: |
Annals of the Institute of Statistical Mathematics. - Springer. - Vol. 65.2013, 2, p. 349-386
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Publisher: |
Springer |
Saved in:
Online Resource
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