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Nonlinear wavelet estimator of the regression function under left-truncated dependent data

Author

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  • Jacobo de Uña-Álvarez
  • Han-Ying Liang
  • Alberto Rodríguez-Casal

Abstract

In this paper, we define a new nonlinear wavelet-based estimator of the regression function under random left-truncation. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the observations form a stationary α-mixing sequence. The nonlinear wavelet-based estimator of the covariate's density is considered as well. Unlike for kernel estimators, the MISE expression of the wavelet-based estimators is not affected by the presence of discontinuities in the curves. The finite sample behaviour of the proposed estimators is explored through simulations.

Suggested Citation

  • Jacobo de Uña-Álvarez & Han-Ying Liang & Alberto Rodríguez-Casal, 2010. "Nonlinear wavelet estimator of the regression function under left-truncated dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(3), pages 319-344.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:3:p:319-344
    DOI: 10.1080/10485250903469736
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    Cited by:

    1. Carolina Costa Mota Paraíba & Natalia Bochkina & Carlos Alberto Ribeiro Diniz, 2018. "Bayesian truncated beta nonlinear mixed-effects models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 320-346, January.
    2. Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2011. "Local polynomial estimation of a conditional mean function with dependent truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 653-677, November.
    3. Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2012. "Asymptotic properties of conditional distribution estimator with truncated, censored and dependent data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 790-810, December.

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