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Density deconvolution for generalized skew-symmetric distributions

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  • Cornelis J. Potgieter

    (Department of Mathematics, Texas Christian University
    Department of Statistics, University of Johannesburg)

Abstract

The density deconvolution problem is considered for random variables assumed to belong to the generalized skew-symmetric (GSS) family of distributions. The approach is semiparametric in that the symmetric component of the GSS distribution is assumed known, and the skewing function capturing deviation from the symmetric component is estimated using a deconvolution kernel approach. This requires the specification of a bandwidth parameter. The mean integrated square error (MISE) of the GSS deconvolution estimator is derived, and two bandwidth estimation methods based on approximating the MISE are also proposed. A generalized method of moments approach is also developed for estimation of the underlying GSS location and scale parameters. Simulation study results are presented including a comparing the GSS approach to the nonparametric deconvolution estimator. For most simulation settings considered, the GSS estimator is seen to have performance superior to the nonparametric estimator.

Suggested Citation

  • Cornelis J. Potgieter, 2020. "Density deconvolution for generalized skew-symmetric distributions," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.
  • Handle: RePEc:spr:jstada:v:7:y:2020:i:1:d:10.1186_s40488-020-00103-y
    DOI: 10.1186/s40488-020-00103-y
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    References listed on IDEAS

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    1. F. Kahrari & C. S. Ferreira & R. B. Arellano-Valle, 2019. "Skew-Normal-Cauchy Linear Mixed Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 185-202, December.
    2. Arellano-Valle, R.B. & Ozan, S. & Bolfarine, H. & Lachos, V.H., 2005. "Skew normal measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 265-281, October.
    3. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, March.
    4. A. Delaigle & I. Gijbels, 2002. "Estimation of integrated squared density derivatives from a contaminated sample," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 869-886, October.
    5. Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
    6. Adelchi Azzalini & Marc G. Genton & Bruno Scarpa, 2010. "Invariance-based estimating equations for skew-symmetric distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 275-298.
    7. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.
    8. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    9. Kim, Hyoung-Moon & Maadooliat, Mehdi & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2016. "Skewed factor models using selection mechanisms," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 162-177.
    10. A. Guolo, 2008. "A Flexible Approach to Measurement Error Correction in Case–Control Studies," Biometrics, The International Biometric Society, vol. 64(4), pages 1207-1214, December.
    11. Karin K. Chu & Naisyin Wang & Scott Stanley & Noah D. Cohen, 2001. "Statistical Evaluation of the Regulatory Guidelines for Use of Furosemide in Race Horses," Biometrics, The International Biometric Society, vol. 57(1), pages 294-301, March.
    12. Ma, Yanyuan & Genton, Marc G. & Tsiatis, Anastasios A., 2005. "Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 980-989, September.
    13. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi & Ferreira, Clécio S. & Santoro, Karol, 2020. "A two-piece normal measurement error model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    14. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    15. Aurore Delaigle & Peter Hall, 2014. "Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 717-729, June.
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