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On Fixed Design Regression for General Linear Processes
Authors:Wentao Gu  Soyeon Lee
Institution:1. Department of Statistics , Zhejiang Gongshang University , Hangzhou , China zjgsu-guwentao@hotmail.com;3. Department of Mathematics , Occidental College , Los Angeles , California , USA
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
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