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Balanced Confidence Regions Based on Tukey’s Depth and the Bootstrap

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  • Arthur B. Yeh
  • Kesar Singh

Abstract

We propose and study the bootstrap confidence regions for multivariate parameters based on Tukey’s depth. The bootstrap is based on the normalized or Studentized statistic formed from an independent and identically distributed random sample obtained from some unknown distribution in Rq. The bootstrap points are deleted on the basis of Tukey’s depth until the desired confidence level is reached. The proposed confidence regions are shown to be second order balanced in the context discussed by Beran. We also study the asymptotic consistency of Tukey’s depth‐based bootstrap confidence regions. The applicability of the method proposed is demonstrated in a simulation study.

Suggested Citation

  • Arthur B. Yeh & Kesar Singh, 1997. "Balanced Confidence Regions Based on Tukey’s Depth and the Bootstrap," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 639-652.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:3:p:639-652
    DOI: 10.1111/1467-9868.00088
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    Cited by:

    1. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    2. Chau, Van Vinh & Ombao, Hernando & von Sachs, Rainer, 2017. "Data depth and rank-based tests for covariance and spectral density matrices," LIDAM Discussion Papers ISBA 2017019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Einmahl, J.H.J. & Li, Jun & Liu, Regina, 2015. "Bridging Centrality and Extremity : Refining Empirical Data Depth using Extreme Value Statistics," Discussion Paper 2015-020, Tilburg University, Center for Economic Research.
    4. Gloria Gonzalez-Rivera & Yun Luo & Esther Ruiz, 2018. "Prediction Regions for Interval-valued Time Series," Working Papers 201817, University of California at Riverside, Department of Economics.

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