Statistics and Computing

, Volume 24, Issue 3, pp 443–460 | Cite as

LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation

  • Ana Arribas-Gil
  • Karine Bertin
  • Cristian Meza
  • Vincent Rivoirard
Article

Abstract

Parametric nonlinear mixed effects models (NLMEs) are now widely used in biometrical studies, especially in pharmacokinetics research and HIV dynamics models, due to, among other aspects, the computational advances achieved during the last years. However, this kind of models may not be flexible enough for complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been proposed as an extension of NLMEs. These models are a good compromise and retain nice features of both parametric and nonparametric models resulting in more flexible models than standard parametric NLMEs. However, SNMMs are complex models for which estimation still remains a challenge. Previous estimation procedures are based on a combination of log-likelihood approximation methods for parametric estimation and smoothing splines techniques for nonparametric estimation. In this work, we propose new estimation strategies in SNMMs. On the one hand, we use the Stochastic Approximation version of EM algorithm (SAEM) to obtain exact ML and REML estimates of the fixed effects and variance components. On the other hand, we propose a LASSO-type method to estimate the unknown nonlinear function. We derive oracle inequalities for this nonparametric estimator. We combine the two approaches in a general estimation procedure that we illustrate with simulations and through the analysis of a real data set of price evolution in on-line auctions.

Keywords

LASSO Nonlinear mixed-effects model On-line auction SAEM algorithm Semiparametric estimation 

Supplementary material

11222_2013_9380_MOESM1_ESM.pdf (130 kb)
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ana Arribas-Gil
    • 1
  • Karine Bertin
    • 2
  • Cristian Meza
    • 2
  • Vincent Rivoirard
  1. 1.Departamento de EstadísticaUniversidad Carlos III de MadridGetafeSpain
  2. 2.CIMFAV-Facultad de IngenieríaUniversidad de ValparaísoValparaísoChile

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