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Quadratic errors for nonparametric estimates under dependence

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  • Vieu, Philippe
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    Abstract

    We investigate nonparametric curve estimation (including density, distribution, hazard, conditional density, and regression functions estimation) by kernel methods when the observed data satisfy a strong mixing condition. In a first attempt we show asymptotic equivalence of average square errors, integrated square errors, and mean integrated square errors. These results are extensions to dependent data of several works, in particular of those by Marron and Härdle (1986, J. Multivariate Anal. 20 91-113). Then we give precise asymptotic evaluations of these errors.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 39 (1991)
    Issue (Month): 2 (November)
    Pages: 324-347

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    Handle: RePEc:eee:jmvana:v:39:y:1991:i:2:p:324-347

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    Related research

    Keywords: functional estimation kernel methods [alpha]-mixing condition quadratic errors;

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    Cited by:
    1. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    2. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2005. "Nonparametric estimation of time varying parameters under shape restrictions," Journal of Econometrics, Elsevier, vol. 126(1), pages 53-77, May.
    3. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    4. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(2), pages 293-320, June.
    5. É. Youndjé & P. Sarda & P. Vieu, 1996. "Optimal smooth hazard estimates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 5(2), pages 379-394, December.
    6. Bosq, Denis, 1995. "Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 339-347, March.
    7. Quintela-del-Rio, Alejandro, 2007. "Plug-in bandwidth selection in kernel hazard estimation from dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5800-5812, August.
    8. Estévez-Pérez, Graciela, 2002. "On convergence rates for quadratic errors in kernel hazard estimation," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 231-241, April.

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