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Quadratic errors for nonparametric estimates under dependence

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  • Vieu, Philippe

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.

Suggested Citation

  • Vieu, Philippe, 1991. "Quadratic errors for nonparametric estimates under dependence," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 324-347, November.
  • Handle: RePEc:eee:jmvana:v:39:y:1991:i:2:p:324-347
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    Citations

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    Cited by:

    1. 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.
    2. 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;Sociedad de Estadística e Investigación Operativa, vol. 5(2), pages 379-394, December.
    3. 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.
    4. Vieu, Philippe & Sperlich, Stefan & Rodriguez Poo, Juan M., 2000. "Semiparametric estimation of weak and strong separable models," DES - Working Papers. Statistics and Econometrics. WS 10064, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Orbe Mandaluniz, Susan & Ferreira García, María Eva & Rodríguez Poo, Juan M., 2001. "Nonparametric estimation of time varying parameters under shape restrictions," BILTOKI 2001-02, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    6. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    7. 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.
    8. 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;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    9. 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.
    10. 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.
    11. Liebscher, Eckhard, 1996. "Strong convergence of sums of [alpha]-mixing random variables with applications to density estimation," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 69-80, December.
    12. 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.

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