## Article

#### Title: Optimal Smoothing with Correlated Data

##### Issue: Volume 70 Series A Part 1 Year 2008
###### Abstract
Penalized likelihood method offers versatile smoothing techniques in a variety of stochastic settings, and the proper selection of the smoothing parameters and other tuning parameters is crucial to the practical performance of penalized likelihood estimates. In this article, we study the selection of the smoothing parameters and the correlation parameters in penalized likelihood regression with correlated data. We propose a simple modification of Mallows’ $C_L$ to accommodate the correlation parameters, and derive a profiled version for use with unknown variance. The proposed methods are shown to be optimal in a certain sense through asymptotic analysis and numerical simulations. Real-data example is also presented and related issues discussed.