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Bivariate deconvolution with SIMEX: an application to mapping Alaska earthquake density

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  • Julie McIntyre
  • Ronald P. Barry

Abstract

Constructing spatial density maps of seismic events, such as earthquake hypocentres, is complicated by the fact that events are not located precisely. In this paper, we present a method for estimating density maps from event locations that are measured with error. The estimator is based on the simulation--extrapolation method of estimation and is appropriate for location errors that are either homoscedastic or heteroscedastic. A simulation study shows that the estimator outperforms the standard estimator of density that ignores location errors in the data, even when location errors are spatially dependent. We apply our method to construct an estimated density map of earthquake hypocenters using data from the Alaska earthquake catalogue.

Suggested Citation

  • Julie McIntyre & Ronald P. Barry, 2012. "Bivariate deconvolution with SIMEX: an application to mapping Alaska earthquake density," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 297-308, April.
  • Handle: RePEc:taf:japsta:v:39:y:2012:i:2:p:297-308
    DOI: 10.1080/02664763.2011.586683
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    References listed on IDEAS

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    1. Christian Wagner & Ulrich Stadtmüller, 2008. "Asymptotics for TAYLEX and SIMEX estimators in deconvolution of densities," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 507-522.
    2. Lionel Cucala, 2008. "Intensity Estimation for Spatial Point Processes Observed with Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 322-334, June.
    3. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
    4. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    5. Staudenmayer, John & Ruppert, David & Buonaccorsi, John P., 2008. "Density Estimation in the Presence of Heteroscedastic Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 726-736, June.
    6. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
    7. Meister, Alexander, 2006. "Estimating the support of multivariate densities under measurement error," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1702-1717, September.
    8. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
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