Journal
ANNALS OF STATISTICS
Volume 40, Issue 3, Pages 1376-1402Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/12-AOS1010
Keywords
Information criterion; locally stationary processes; nonparametric hypothesis testings; time-varying coefficient models; variable selection
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Funding
- NSF [DMS-09-06073]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0906073] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1106790] Funding Source: National Science Foundation
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We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a n(1/2)-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.
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