On Fixed Design Regression for General Linear Processes

Abstract

This article is concerned with recovering a regression function g(x) on the basis of noisy observations taken at design points x _i . The corresponding observations are corrupted by additive dependent noise induced by a general linear process. The regression function is estimated by a smoother, which is shown to have an asymptotic multivariate normal distribution at multiple points. The problem of finding confidence bands for g(x) is discussed. An illustrative example is also exhibited. The results for finite samples are evaluated by computer simulations.

Keywords:

• Asymptotic normality
• Confidence intervals
• Design points
• Linear process

Mathematics Subject Classification:

• Primary 62G05
• Secondary 60J25, 62J02

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments.