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Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes

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  • Masry, E.

Abstract

We consider the estimation of the multivariate probability density functions of stationary random processes from noisy observations. The asymptotic normality of kernel-type deconvolution estimators is established for various classes of mixing processes. Classes of noise characteristic functions both with algebraic and with exponential decay are studied.

Suggested Citation

  • Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January.
    • Handle: RePEc:eee:jmvana:v:44:y:1993:i:1:p:47-68
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    Cited by:

    1. Ming Yuan, 2003. "Deconvolving Multivariate Density from Random Field," Statistical Inference for Stochastic Processes, Springer, vol. 6(2), pages 135-153, May.
    2. 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).
    3. Marianna Pensky & Ahmed Zayed, 2002. "Density Deconvolution of Different Conditional Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 701-712, September.
    4. 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.
    5. Hao Dong & Taisuke Otsu & Luke Taylor, 2023. "Bandwidth selection for nonparametric regression with errors-in-variables," Econometric Reviews, Taylor & Francis Journals, vol. 42(4), pages 393-419, April.
    6. 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.
    7. 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).
    8. Yang Zu, 2015. "A Note on the Asymptotic Normality of the Kernel Deconvolution Density Estimator with Logarithmic Chi-Square Noise," Econometrics, MDPI, vol. 3(3), pages 1-16, July.
    9. Christian Hesse, 1995. "Deconvolving a density from contaminated dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 645-663, December.
    10. 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.
    11. Mynbaev, Kairat & Martins-Filho, Carlos, 2015. "Consistency and asymptotic normality for a nonparametric prediction under measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 166-188.
    12. 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.
    13. 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.
    14. 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.
    15. D.A. Ioannides & D.P. Papanastassiou, 2001. "Estimating the Distribution Function of a Stationary Process Involving Measurement Errors," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 181-198, May.
    16. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.
    17. 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.
    18. van Es, A. J. & Kok, A. R., 1998. "Simple kernel estimators for certain nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 151-160, August.

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