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Bootstrapping in non-regular smooth function models

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  • Giurcanu, Mihai C.

Abstract

We study the large sample behavior of the standard bootstrap, the m-out-of-n bootstrap, and the oracle bootstrap (Giurcanu and Presnell, 2009) [14] percentile confidence intervals in non-regular smooth function models. We show that the oracle bootstrap percentile confidence intervals are consistent while the standard bootstrap and the m-out-of-n bootstrap confidence intervals are inconsistent. Further analysis of coverage probabilities reveals that, for large samples, the iterated oracle bootstrap percentile confidence intervals are more accurate than their non-iterated versions. We also describe the large sample local behavior of the bootstrap confidence intervals for parameter values near the points of inconsistency of the standard bootstrap. In a simulation study, we describe the finite sample local behavior of various bootstrap confidence intervals.

Suggested Citation

  • Giurcanu, Mihai C., 2012. "Bootstrapping in non-regular smooth function models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 78-93.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:78-93
    DOI: 10.1016/j.jmva.2012.04.016
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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-517, October.
    3. Richard Samworth, 2003. "A note on methods of restoring consistency to the bootstrap," Biometrika, Biometrika Trust, vol. 90(4), pages 985-990, December.
    4. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    5. Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 1-24, March.
    6. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    7. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
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    Cited by:

    1. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    2. Mihai C. Giurcanu, 2017. "Oracle M-Estimation for Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 479-504, May.

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