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Smoothed and iterated bootstrap confidence regions for parameter vectors

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  • Ghosh, Santu
  • Polansky, Alan M.

Abstract

The construction of confidence regions for parameter vectors is a difficult problem in the nonparametric setting, particularly when the sample size is not large. We focus on bootstrap ellipsoidal confidence regions. The bootstrap has shown promise in solving this problem, but empirical evidence often indicates that the bootstrap percentile method has difficulty in maintaining the correct coverage probability, while the bootstrap percentile-t method may be unstable, often resulting in very large confidence regions. This paper considers the smoothed and iterated bootstrap methods to construct the bootstrap percentile method ellipsoidal confidence region. The smoothed bootstrap method is based on a multivariate kernel density estimator. An optimal bandwidth matrix is established for the smoothed bootstrap procedure that reduces the coverage error of the bootstrap percentile method. We also provide an analytical adjustment to the nominal level to reduce the computational cost of the iterated bootstrap method. Simulations demonstrate that the methods can be successfully applied in practice.

Suggested Citation

  • Ghosh, Santu & Polansky, Alan M., 2014. "Smoothed and iterated bootstrap confidence regions for parameter vectors," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 171-182.
    • Handle: RePEc:eee:jmvana:v:132:y:2014:i:c:p:171-182
    DOI: 10.1016/j.jmva.2014.08.003
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    References listed on IDEAS

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    1. Polansky, Alan M., 2001. "Bandwidth selection for the smoothed bootstrap percentile method," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 333-349, May.
    2. Guerra, Rudy & Polansky, Alan M. & Schucany, William R., 1997. "Smoothed bootstrap confidence intervals with discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 163-176, December.
    3. Alan M. Polansky & William. R. Schucany, 1997. "Kernel Smoothing to Improve Bootstrap Confidence Intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 821-838.
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    Cited by:

    1. Santu Ghosh & Alan M. Polansky, 2022. "Large-Scale Simultaneous Testing Using Kernel Density Estimation," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 808-843, August.

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