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

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  • Vidal-Sanz, José 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, José 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
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    1. Vidal-Sanz, José 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.
    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. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

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    2. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    3. 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.
    4. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    5. 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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