A penalized spline approach to functional mixed effects model analysis.

Web-based Supplementary Materials for “A Penalized spline approach to functional mixed effects model analysis” by Huaihou Chen and Yuanjia Wang Semiparametric estimation of the within-subject vari- ation

Simultaneous Confidence Bands for Penalized Spline Estimators

In this paper we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (i) as a standard (fixed effect) nonparametric model, (ii) using the mixed model framework with the spline coefficients as random effects and (iii) a Bayesian approach. The volume-of-tube formula is applied for the first two methods and co...

A note on bimodality in the log-likelihood function for penalized spline mixed models

For a smoothing spline or general penalized spline model, the smoothing parameter can be estimated using residual maximum likelihood (REML) methods by expressing the spline in the form of a mixed model. The possibility of bimodality in the profile log-likelihood function for the smoothing parameter of these penalized spline mixed models is demonstrated. A canonical transformation into independe...

Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...

Using single-index ODEs to study dynamic gene regulatory network

With the development of biotechnology, high-throughput studies on protein-protein, protein-gene, and gene-gene interactions become possible and attract remarkable attention. To explore the interactions in dynamic gene regulatory networks, we propose a single-index ordinary differential equation (ODE) model and develop a variable selection procedure. We employ the smoothly clipped absolute devia...