IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v80y2018i1d10.1007_s13171-018-0154-6.html
   My bibliography  Save this article

Uncertainty Quantification in Robust Inference for Irregularly Spaced Spatial Data Using Block Bootstrap

Author

Listed:
  • S. N. Lahiri

    (North Carolina State University)

Abstract

This paper deals with uncertainty quantification (UQ) for a class of robust estimators of population parameters of a stationary, multivariate random field that is observed at a finite number of locations s1,…, sn, generated by a stochastic design. The class of robust estimators considered here is given by the so-called M-estimators that in particular include robust estimators of location, scale, linear regression parameters, as well as the maximum likelihood and pseudo maximum likelihood estimators, among others. Finding practically useful UQ measures, both in terms of standard errors of the point estimators as well as interval estimation for the parameters is a difficult problem due to presence of inhomogeneous dependence among irregularly spaced spatial observations. Exact and asymptotic variances of such estimators have a complicated form that depends on the autocovariance function of the random field, the spatial sampling density, and also on the relative rate of growth of the sample size versus the volume of the sampling region. Similar complex interactions of these factors are also present in the sampling distributions of these estimators which makes exact calibration of confidence intervals impractical. Here it is shown that a version of the spatial block bootstrap can be used to produce valid UQ measures, both in terms of estimation of the standard error as well as interval estimation. A key advantage of the proposed method is that it provides valid approximations in very general settings without requiring any explicit adjustments for spatial sampling structures and without requiring explicit estimation of the covariance function and of the spatial sampling density.

Suggested Citation

  • S. N. Lahiri, 2018. "Uncertainty Quantification in Robust Inference for Irregularly Spaced Spatial Data Using Block Bootstrap," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 173-221, December.
  • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-018-0154-6
    DOI: 10.1007/s13171-018-0154-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-018-0154-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13171-018-0154-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. Lahiri & Kanchan Mukherjee, 2004. "Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 225-250, June.
    2. Lahiri, Soumendra Nath, 1996. "On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 42-59, January.
    3. Lahiri, S. N., 1993. "On the moving block bootstrap under long range dependence," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 405-413, December.
    4. Bradley, Richard C., 1989. "A caution on mixing conditions for random fields," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 489-491, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Richard C. Bradley, 2001. "A Stationary Rho-Mixing Markov Chain Which Is Not “Interlaced” Rho-Mixing," Journal of Theoretical Probability, Springer, vol. 14(3), pages 717-727, July.
    2. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    3. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    4. Choi, Ji-Eun & Shin, Dong Wan, 2019. "Moving block bootstrapping for a CUSUM test for correlation change," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 95-106.
    5. Daniel Nordman, 2008. "An empirical likelihood method for spatial regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 351-363, November.
    6. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    7. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Amilcar Velez, 2023. "The Local Projection Residual Bootstrap for AR(1) Models," Papers 2309.01889, arXiv.org, revised Feb 2024.
    9. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    10. Romano, Joseph P. & Wolf, Michael, 2001. "Improved nonparametric confidence intervals in time series regressions," DES - Working Papers. Statistics and Econometrics. WS ws010201, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. S. Lahiri & Kanchan Mukherjee, 2004. "Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 225-250, June.
    12. Kristoufek, Ladislav, 2019. "Are the crude oil markets really becoming more efficient over time? Some new evidence," Energy Economics, Elsevier, vol. 82(C), pages 253-263.
    13. Andrea Pallini, 2000. "Resampling configurations of points through coding schemes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 9(1), pages 159-182, January.
    14. Arteche, Josu & Orbe, Jesus, 2016. "A bootstrap approximation for the distribution of the Local Whittle estimator," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 645-660.
    15. Daniel J. Nordman & Philipp Sibbertsen & Soumendra N. Lahiri, 2007. "Empirical likelihood confidence intervals for the mean of a long‐range dependent process," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 576-599, July.
    16. Franco, Glaura C. & Reisen, Valderio A., 2007. "Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 546-562.
    17. Kim, Young Min & Nordman, Daniel J., 2013. "A frequency domain bootstrap for Whittle estimation under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 405-420.
    18. Burton, Robert M. & Steif, Jeffrey E., 1995. "Quite weak Bernoulli with exponential rate and percolation for random fields," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 35-55, July.
    19. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
    20. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-018-0154-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.