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Strong consistency and rates for deconvolution of multivariate densities of stationary processes

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  • Masry, Elias

Abstract

We consider the estimation of the multivariate probability density functions of stationary random processes from noisy observations. The strong consistency and almost sure convergence rates for kernel-type deconvolution estimators is established for strongly mixing processes. The dependence of the a.s. convergence rates on the noise distribution is examined; both ordinary and super smooth noise distributions are considered.

Suggested Citation

  • Masry, Elias, 1993. "Strong consistency and rates for deconvolution of multivariate densities of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 53-74, August.
    • Handle: RePEc:eee:spapps:v:47:y:1993:i:1:p:53-74
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    Cited by:

    1. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    2. Chesneau, Christophe & Fadili, Jalal & Maillot, Bertrand, 2015. "Adaptive estimation of an additive regression function from weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 77-94.
    3. Zhou, Yong & Liang, Hua, 2000. "Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 136-154, April.
    4. Van Es, Bert & Spreij, Peter, 2011. "Estimation of a multivariate stochastic volatility density by kernel deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 683-697, March.
    5. Denis Belomestny & Mathias Trabs & Alexandre Tsybakov, 2017. "Sparse covariance matrix estimation in high-dimensional deconvolution," Working Papers 2017-25, Center for Research in Economics and Statistics.
    6. Lacour, Claire, 2008. "Adaptive estimation of the transition density of a particular hidden Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 787-814, May.
    7. Otsu, Taisuke & Taylor, Luke, 2021. "Specification Testing For Errors-In-Variables Models," Econometric Theory, Cambridge University Press, vol. 37(4), pages 747-768, August.
    8. Rachdi, Mustapha & Sabre, Rachid, 2000. "Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 105-114, April.
    9. Song, Weixing, 2008. "Model checking in errors-in-variables regression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2406-2443, November.
    10. Yousri Slaoui, 2021. "Data-driven Deconvolution Recursive Kernel Density Estimators Defined by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 312-352, February.
    11. Guo, Linruo & Song, Weixing & Shi, Jianhong, 2022. "Estimating multivariate density and its derivatives for mixed measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    12. Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.
    13. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    14. Seçil Yalaz, 2019. "Multivariate partially linear regression in the presence of measurement error," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 123-135, March.
    15. Guillermo Basulto-Elias & Alicia L. Carriquiry & Kris Brabanter & Daniel J. Nordman, 2021. "Bivariate Kernel Deconvolution with Panel Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 122-151, May.
    16. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
    17. Ioannides, D. A. & Alevizos, P. D., 1997. "Nonparametric regression with errors in variables and applications," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 35-43, February.

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