Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model

• Main Authors: Behdad Mostafaiy, Mohammad Reza Faridrohani
• Format: Article
• Language: English
• Published: Atlantis Press 2017-08-01
• Series: Journal of Statistical Theory and Applications (JSTA)
• Subjects: Functional varying coefficient model; Longitudinal data Analysis; Rate of convergence; Regularization; Reproducing kernel Hilbert space; Sparsity.
• Online Access: https://www.atlantis-press.com/article/25883866.pdf

In the present paper, we study functional varying coefficient model in which both the response and the predictor are functions. We give estimates of the intercept and the slope functions in the case that the observations are sparse and noise-contaminated longitudinal data by using least squares representation of the model parameters. To estimate the parameter functions involved in the representation, we use a regularization method in some reproducing kernel Hilbert spaces. As we will see, our procedure is easy to implement. Also, we obtain the convergence rates of the estimators in the <i>L</i>²-sense. These convergence rates establish that the procedure performs well, especially, when sampling frequency or sample size increases.