Keywords: Varying coefficient model ; Minimax rate of convergence; Smoothing splines estimates; Longitudinal data
Smoothing splines estimates for varying coefficient models were proposed by Hastie and Tibshirani (1993) to address repeated measurements. Although there exist efficient algorithms, e.g., the backfitting schemes, it remains unclear about the sampling properties of this estimator. We obtain sharp results on the minimax rates of convergences and show that smoothing spline estimators achieve the optimal rates of convergence for both prediction and estimation problems. Numerical results are obtained to demonstrate the theoretical developments.