IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v99y2008i9p1962-1984.html
   My bibliography  Save this article

Properties of spatial cross-periodograms using fixed-domain asymptotics

Author

Listed:
  • Lim, Chae Young
  • Stein, Michael

Abstract

Cross-periodograms can be used to study a multivariate spatial process observed on a lattice. For spatial data, it is often appropriate to study asymptotic properties of statistical procedures under fixed-domain asymptotics in which the number of observations increases in a fixed region while shrinking distances between neighboring observations. Using fixed-domain asymptotics, we prove relative asymptotic unbiasedness and relative consistency of a smoothed cross-periodogram after appropriate filtering of the data. In addition, we show that smoothed cross-periodograms are asymptotically normal when the process is stationary multivariate Gaussian with appropriate assumptions on high-frequency behavior of the spectral density.

Suggested Citation

  • Lim, Chae Young & Stein, Michael, 2008. "Properties of spatial cross-periodograms using fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1962-1984, October.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:1962-1984
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00040-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. István Fazekas & Alexey Chuprunov, 2006. "Asymptotic Normality of Kernel Type Density Estimators for Random Fields," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 161-178, July.
    2. Hao Zhang & Dale L. Zimmerman, 2005. "Towards reconciling two asymptotic frameworks in spatial statistics," Biometrika, Biometrika Trust, vol. 92(4), pages 921-936, December.
    3. Montserrat Fuentes, 2002. "Spectral methods for nonstationary spatial processes," Biometrika, Biometrika Trust, vol. 89(1), pages 197-210, March.
    4. Furrer, Reinhard, 2005. "Covariance estimation under spatial dependence," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 366-381, June.
    5. Jun Zhu & S. Lahiri, 2007. "Bootstrapping the Empirical Distribution Function of a Spatial Process," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 107-145, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wu, Wei-Ying & Lim, Chae Young & Xiao, Yimin, 2013. "Tail estimation of the spectral density for a stationary Gaussian random field," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 74-91.
    2. Guinness, Joseph, 2022. "Nonparametric spectral methods for multivariate spatial and spatial–temporal data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    3. Zhou, Yuzhen & Xiao, Yimin, 2018. "Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 56-72.

    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. Meyer, Marco & Jentsch, Carsten & Kreiss, Jens-Peter, 2015. "Baxter`s inequality and sieve bootstrap for random fields," Working Papers 15-06, University of Mannheim, Department of Economics.
    2. Tatiyana V. Apanasovich & David Ruppert & Joanne R. Lupton & Natasa Popovic & Nancy D. Turner & Robert S. Chapkin & Raymond J. Carroll, 2008. "Aberrant Crypt Foci and Semiparametric Modeling of Correlated Binary Data," Biometrics, The International Biometric Society, vol. 64(2), pages 490-500, June.
    3. Marcelo Cunha & Dani Gamerman & Montserrat Fuentes & Marina Paez, 2017. "A non-stationary spatial model for temperature interpolation applied to the state of Rio de Janeiro," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 919-939, November.
    4. Kiselák, Jozef & Stehlík, Milan, 2008. "Equidistant and D-optimal designs for parameters of Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1388-1396, September.
    5. Girard, Didier A., 2020. "Asymptotic near-efficiency of the “Gibbs-energy (GE) and empirical-variance” estimating functions for fitting Matérn models - II: Accounting for measurement errors via “conditional GE mean”," Statistics & Probability Letters, Elsevier, vol. 162(C).
    6. Peter J. Brockwell & Yasumasa Matsuda, 2015. "Levy-driven CARMA Random Fields on Rn," TERG Discussion Papers 339, Graduate School of Economics and Management, Tohoku University.
    7. Martin Tingley & Benjamin Shaby, 2015. "Comments on: Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 47-53, March.
    8. Joaquim Henriques Vianna Neto & Alexandra M. Schmidt & Peter Guttorp, 2014. "Accounting for spatially varying directional effects in spatial covariance structures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 103-122, January.
    9. Maroussa Zagoraiou & Alessandro Baldi Antognini, 2009. "Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 583-600, September.
    10. Fuentes, Montserrat, 2005. "A formal test for nonstationarity of spatial stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 30-54, September.
    11. Li, Yang & Zhu, Zhengyuan, 2016. "Modeling nonstationary covariance function with convolution on sphere," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 233-246.
    12. Bachoc, François & Lagnoux, Agnès & Nguyen, Thi Mong Ngoc, 2017. "Cross-validation estimation of covariance parameters under fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 42-67.
    13. Wenpin Tang & Lu Zhang & Sudipto Banerjee, 2021. "On identifiability and consistency of the nugget in Gaussian spatial process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1044-1070, November.
    14. Alain Pirotte & Jesús Mur, 2017. "Neglected dynamics and spatial dependence on panel data: consequences for convergence of the usual static model estimators," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(2-3), pages 202-229, July.
    15. Christopher K. Wikle, 2003. "Hierarchical Models in Environmental Science," International Statistical Review, International Statistical Institute, vol. 71(2), pages 181-199, August.
    16. Ashton Wiens & Douglas Nychka & William Kleiber, 2020. "Modeling spatial data using local likelihood estimation and a Matérn to spatial autoregressive translation," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.
    17. Werner Müller & Milan Stehlík, 2009. "Issues in the optimal design of computer simulation experiments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 163-177, March.
    18. Tata Subba Rao & Granville Tunnicliffe Wilson & Joao Jesus & Richard E. Chandler, 2017. "Inference with the Whittle Likelihood: A Tractable Approach Using Estimating Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 204-224, March.
    19. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    20. Tae Kim & Jeong Park & Gyu Song, 2010. "An asymptotic theory for the nugget estimator in spatial models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 181-195.

    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:eee:jmvana:v:99:y:2008:i:9:p:1962-1984. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.