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Test inversion bootstrap confidence intervals

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  • J. Carpenter

Abstract

In this paper we explore the theoretical and practical implications of using bootstrap test inversion to construct confidence intervals. In the presence of nuisance parameters, we show that the coverage error of such intervals is O(n−1/2) which may be reduced to O(n−1) if a Studentized statistic is used. We present three simulation studies and compare the performance of test inversion methods with established methods on the problem of estimating a confidence interval for the dose–response parameter in models of the Japanese atomic bomb survivors data.

Suggested Citation

  • J. Carpenter, 1999. "Test inversion bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 159-172.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:1:p:159-172
    DOI: 10.1111/1467-9868.00169
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    Cited by:

    1. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    2. Hidalgo, Javier & Lee, Jungyoon & Seo, Myung Hwan, 2019. "Robust inference for threshold regression models," Journal of Econometrics, Elsevier, vol. 210(2), pages 291-309.
    3. van Giersbergen, Noud P. A. & Kiviet, Jan F., 2002. "How to implement the bootstrap in static or stable dynamic regression models: test statistic versus confidence region approach," Journal of Econometrics, Elsevier, vol. 108(1), pages 133-156, May.
    4. Lee, Stephen M.S. & Young, G. Alastair, 2005. "Parametric bootstrapping with nuisance parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 143-153, February.
    5. G. Alastair Young, 2003. "Better bootstrapping by constrained prepivoting," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 227-242.
    6. Gatta, Valerio & Marcucci, Edoardo & Scaccia, Luisa, 2015. "On finite sample performance of confidence intervals methods for willingness to pay measures," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 169-192.

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