IDEAS home Printed from https://ideas.repec.org/p/cte/wbrepe/wb072606.html
   My bibliography  Save this paper

Automatic spectral density estimation for Random fields on a lattice via bootstrap

Author

Listed:
  • Vidal-Sanz, Jose M.

Abstract

This paper considers the nonparametric estimation of spectral densities for second order stationary random fields on a d-dimensional lattice. I discuss some drawbacks of standard methods, and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. I prove uniform consistency and study the uniform asymptotic distribution, when the optimal smoothing number is estimated from the sampled data.

Suggested Citation

  • Vidal-Sanz, Jose M., 2007. "Automatic spectral density estimation for Random fields on a lattice via bootstrap," DEE - Working Papers. Business Economics. WB wb072606, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    • Handle: RePEc:cte:wbrepe:wb072606
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/83508d2c-09c9-4df3-a0a2-89afe505da9e/content
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Delgado, Miguel A. & Vidal-Sanz, Jose M., 2002. "Averaged Singular Integral Estimation as a Bias Reduction Technique," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 127-137, January.
    2. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    3. Jose Vidal-Sanz, 2009. "Automatic spectral density estimation for random fields on a lattice via bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 96-114, May.
    4. Robinson, P.M. & Vidal Sanz, J., 2006. "Modified Whittle estimation of multilateral models on a lattice," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1090-1120, May.
    5. Vidal-Sanz, Jose M., 2004. "Pointwise universal consistency of nonparametric linear estimators," DEE - Working Papers. Business Economics. WB wb045821, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    6. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
    7. E. Renshaw & E. D. Ford, 1983. "The Interpretation of Process from Pattern Using Two‐Dimensional Spectral Analysis: Methods and Problems of Interpretation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(1), pages 51-63, March.
    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. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    2. Jose Vidal-Sanz, 2009. "Automatic spectral density estimation for random fields on a lattice via bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 96-114, May.
    3. repec:esx:essedp:767 is not listed on IDEAS
    4. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    5. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.

    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. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    2. repec:esx:essedp:767 is not listed on IDEAS
    3. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    4. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.
    5. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    6. Chambers, Marcus J. & Ercolani, Joanne S. & Taylor, A.M. Robert, 2014. "Testing for seasonal unit roots by frequency domain regression," Journal of Econometrics, Elsevier, vol. 178(P2), pages 243-258.
    7. Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
    8. Wouter J. Den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
    9. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(4), pages 743-755, August.
    10. Javier Hidalgo, 2003. "A Bootstrap Causality Test for Covariance Stationary Processes," STICERD - Econometrics Paper Series 462, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
    12. Peter M Robinson, 2006. "Nonparametric Spectrum Estimation for SpatialData," STICERD - Econometrics Paper Series 498, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Hidalgo, Javier, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.
    14. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
    15. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    16. Yasumasa Matsuda & Yoshihiro Yajima, 2004. "On testing for separable correlations of multivariate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 501-528, July.
    17. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    18. Renshaw, Eric & Sarkka, Aila, 2001. "Gibbs point processes for studying the development of spatial-temporal stochastic processes," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 85-105, March.
    19. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    20. Jentsch, Carsten & Subba Rao, Suhasini, 2015. "A test for second order stationarity of a multivariate time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 124-161.
    21. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.

    More about this item

    Keywords

    Spatial data;

    JEL classification:

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:cte:wbrepe:wb072606. 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: Ana Poveda (email available below). General contact details of provider: http://www.business.uc3m.es/es/index .

    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.