LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation
- 664 Downloads
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.
KeywordsLASSO Nonlinear mixed-effects model On-line auction SAEM algorithm Semiparametric estimation
The authors would like to thank the anonymous Associate Editor and two referees for valuable comments and suggestions.
The research of Ana Arribas-Gil is supported by projects MTM2010-17323 and ECO2011-25706, Spain.
The research of Karine Bertin is supported by projects FONDECYT 1090285 and ECOS/CONICYT C10E03 2010, Chile.
The research of Cristian Meza is supported by project FONDECYT 11090024, Chile.
The research of Vincent Rivoirard is partly supported by the french Agence Nationale de la Recherche (ANR 2011 BS01 010 01 projet Calibration).
- Bunea, F.: Consistent selection via the Lasso for high dimensional approximating regression models. In: Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh. Inst. Math. Stat. Collect., vol. 3, pp. 122–137. Inst. Math. Statist., Beachwood (2008) CrossRefGoogle Scholar
- van de Geer, S.: ℓ 1-regularization in high-dimensional statistical models. In: Proceedings of the International Congress of Mathematicians, vol. IV, pp. 2351–2369. Hindustan Book Agency, New Delhi (2010) Google Scholar
- Sklar, J.C., Wu, J., Meiring, W., Wang, Y.: Non-parametric regression with basis selection from multiple libraries. Technometrics (2012, accepted) Google Scholar
- Wang, Y., Ke, C.: Assist: A suite of s functions implementing spline smoothing techniques (2004). http://wwwpstatucsbedu/faculty/yuedong/assistpdf