Asymptotic normality of spline estimator when the errors are a linear stationary process

Abstract

Smoothing splines are considered for estimating an unknown regular function when the errors in the observations are dependent This dependence is modelled here by assuming that the errors form a linear stationary process defined over some sequence of martingale differences. Some statistical properties of the smoothing spline estimator under consideration are studied and mainly its asymptotic normality is established

Keywords:

• Spline regression
• Martingale differences
• Linear stationary process
• Asymptotic normality