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On large deviations in testing simple hypotheses for locally stationary Gaussian processes

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  • Inder Tecuapetla-Gómez
  • Michael Nussbaum

Abstract

We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationary Gaussian processes. This result allows us to find explicitly the rates of exponential decay of the error probabilities of type I and type II for Neyman–Pearson tests. Furthermore, we obtain the analogue of classical results on asymptotic efficiency of tests such as Stein’s lemma and the Chernoff bound, as well as the more general Hoeffding bound concerning best possible joint exponential rates for the two error probabilities. Copyright Springer Science+Business Media B.V. 2012

Suggested Citation

  • Inder Tecuapetla-Gómez & Michael Nussbaum, 2012. "On large deviations in testing simple hypotheses for locally stationary Gaussian processes," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 225-239, October.
    • Handle: RePEc:spr:sistpr:v:15:y:2012:i:3:p:225-239
    DOI: 10.1007/s11203-012-9071-9
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    References listed on IDEAS

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    1. Pavel Gapeev & Uwe Küchler, 2008. "On large deviations in testing Ornstein–Uhlenbeck-type models," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 143-155, June.
    2. Zani, Marguerite, 2002. "Large Deviations for Quadratic Forms of Locally Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 205-228, May.
    3. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    4. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
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