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

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  • Jose Vidal-Sanz

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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.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:testjl:v:18:y:2009:i:1:p:96-114
    DOI: 10.1007/s11749-007-0059-5
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    References listed on IDEAS

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    1. 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.
    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.
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    Cited by:

    1. 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.
    2. repec:esx:essedp:767 is not listed on IDEAS
    3. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    4. 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.

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