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Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series

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  • Masry, Elias

Abstract

The estimation of the multivariate probability density functions f(x1, ... , xd), d >= 1, of a stationary random process {Xi} using wavelet methods is considered. Uniform rates of almost sure convergence over compact subsets of d for densities in the Besov space Bspq are established for strongly mixing processes.

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  • 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.
    • Handle: RePEc:eee:spapps:v:67:y:1997:i:2:p:177-193
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    References listed on IDEAS

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    1. Tran, Lanh Tat, 1992. "Kernel density estimation for linear processes," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 281-296, June.
    2. 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.
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    8. 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.
    9. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
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    Cited by:

    1. Antonio Cosma & Olivier Scaillet & Rainer von Sachs, 2005. "Multiariate Wavelet-based sahpe preserving estimation for dependant observation," FAME Research Paper Series rp144, International Center for Financial Asset Management and Engineering.
    2. Salim Bouzebda & Christophe Chesneau, 2020. "A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods," Stats, MDPI, vol. 3(4), pages 1-9, October.
    3. Rodney V. Fonseca & Aluísio Pinheiro, 2020. "Wavelet estimation of the dimensionality of curve time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1175-1204, October.
    4. Krebs, Johannes T.N., 2018. "Nonparametric density estimation for spatial data with wavelets," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 300-319.
    5. Neumeyer, Natalie, 2007. "A note on uniform consistency of monotone function estimators," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 693-703, April.
    6. Varron, Davit, 2008. "Some asymptotic results on density estimators by wavelet projections," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2517-2521, October.
    7. Neumeyer, Natalie, 2005. "A note on uniform consistency of monotone function estimators," Technical Reports 2005,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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