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On the asymptotic theory of subsampling

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  • Politis, Dimitris N.
  • Romano, Joseph P.
  • Wolf, Michael

Abstract

A general approach to constructing confidence intervals by subsampling was presented in Politis and Romano (1994). The crux of the method is based on recomputing a statistic over subsamples of the data, and these recomputed values are used to build up an estimated sampling distribution. The method works under extremely weak conditions, it applies to independent, identically distributed (LLd.) observations as well as to dependent data situations, such as time series (possible non stationary) , random fields, and marked point processes. In this article, we present some new theorems showing: a new construction for confidence intervals that removes a previous condition, a general theorem showing the validity of subsampling for datadependent choices of the block size, and a general theorem for the construction of hypothesis tests (which is not necessarily derived from a confidence interval construction). The arguments apply to both the Li.d. setting as well as the dependent data case.

Suggested Citation

  • Politis, Dimitris N. & Romano, Joseph P. & Wolf, Michael, 1999. "On the asymptotic theory of subsampling," DES - Working Papers. Statistics and Econometrics. WS 6334, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6334
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    1. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
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    1. Broszkiewicz-Suwaj, E & Makagon, A & Weron, R & Wyłomańska, A, 2004. "On detecting and modeling periodic correlation in financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 196-205.
    2. Chung, EunYi & Romano, Joseph P., 2016. "Multivariate and multiple permutation tests," Journal of Econometrics, Elsevier, vol. 193(1), pages 76-91.
    3. Zheng, Wei & Jin, Yong & Zhang, Guoyi, 2016. "Recursive estimation of time-average variance constants through prewhitening," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 30-37.
    4. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    5. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    6. Chan, Kam Fong & Powell, John G. & Treepongkaruna, Sirimon, 2014. "Currency jumps and crises: Do developed and emerging market currencies jump together?," Pacific-Basin Finance Journal, Elsevier, vol. 30(C), pages 132-157.
    7. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    8. Chang, Christopher C. & Politis, Dimitris N., 2011. "Bootstrap with larger resample size for root-n consistent density estimation with time series data," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 652-661, June.
    9. Politis, Dimitris N. & Romano, Joseph P., 2010. "K-sample subsampling in general spaces: The case of independent time series," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 316-326, February.
    10. Berg, Arthur & McMurry, Timothy L. & Politis, Dimitris N., 2010. "Subsampling p-values," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1358-1364, September.
    11. Lenart, Łukasz, 2013. "Non-parametric frequency identification and estimation in mean function for almost periodically correlated time series," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 252-269.
    12. Linton, Oliver & Whang, Yoon-Jae & Yen, Yu-Min, 2016. "A nonparametric test of a strong leverage hypothesis," Journal of Econometrics, Elsevier, vol. 194(1), pages 153-186.
    13. Hong, Shengjie, 2017. "Inference in semiparametric conditional moment models with partial identification," Journal of Econometrics, Elsevier, vol. 196(1), pages 156-179.
    14. Linton, Oliver & Smetanina, Ekaterina, 2016. "Testing the martingale hypothesis for gross returns," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 664-689.
    15. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2016. "Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach," CREATES Research Papers 2016-27, Department of Economics and Business Economics, Aarhus University.
    16. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators," Journal of Econometrics, Elsevier, vol. 152(1), pages 19-27, September.
    17. Kaido, Hiroaki, 2016. "A dual approach to inference for partially identified econometric models," Journal of Econometrics, Elsevier, vol. 192(1), pages 269-290.

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    Keywords

    Confidence intervals;

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