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Wavelet regression estimation in nonparametric mixed effect models

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  • Angelini, Claudia
  • De Canditiis, Daniela
  • Leblanc, Frédérique

Abstract

We show that a nonparametric estimator of a regression function, obtained as solution of a specific regularization problem is the best linear unbiased predictor in some nonparametric mixed effect model. Since this estimator is intractable from a numerical point of view, we propose a tight approximation of it easy and fast to implement. This second estimator achieves the usual optimal rate of convergence of the mean integrated squared error over a Sobolev class both for equispaced and nonequispaced design. Numerical experiments are presented both on simulated and ERP real data.

Suggested Citation

  • Angelini, Claudia & De Canditiis, Daniela & Leblanc, Frédérique, 2003. "Wavelet regression estimation in nonparametric mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 267-291, May.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:2:p:267-291
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    References listed on IDEAS

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    1. F. Abramovich & T. Sapatinas & B. W. Silverman, 1998. "Wavelet thresholding via a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 725-749.
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    1. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    2. Mariola Sánchez-González & María Durbán & Dae-Jin Lee & Isabel Cañellas & Hortensia Sixto, 2017. "Smooth additive mixed models for predicting aboveground biomass," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 23-41, March.
    3. Ruiz-Medina, María D. & Álvarez-Liébana, Javier, 2019. "Strongly consistent autoregressive predictors in abstract Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 186-201.
    4. Kun Huang & Sijie Zheng & Lijian Yang, 2022. "Inference for dependent error functional data with application to event-related potentials," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1100-1120, December.
    5. M. Rincón & M. Ruiz-Medina, 2012. "Wavelet-RKHS-based functional statistical classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(3), pages 201-217, October.
    6. Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 257-285, September.

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