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Zbl 0862.62069
Tran, Lanh; Roussas, George; Yakowitz, Sidney; Van, B.Truong
(Truong Van, B.)
Fixed-design regression for linear time series. (English)
[J] Ann. Stat. 24, No.3, 975-991 (1996). ISSN 0090-5364

Summary: This investigation is concerned with recovering a regression function $g(x_i)$ on the basis of noisy observations taken at uniformly spaced design points $x_i$. It is presumed that the corresponding observations are corrupted by additive dependent noise, and that the noise is, in fact, induced by a general linear process in which the summand law can be discrete, as well as continuously distributed. Discreteness induces a complication because such noise is not known to be strong mixing, the postulate by which regression estimates are often shown to be asymptotically normal. In fact, as cited, there are processes of this character which have been proven not to be strong mixing.\par The main analytic result of this study is that, in general circumstances which include the non-strong mixing example, the smoothers we propose are asymptotically normal. Some motivation is offered, and a simple illustrative example calculation concludes this investigation. The innovative elements of this work, mainly, consist of encompassing models with discrete noise, important in practical applications, and in dispensing with mixing assumptions. The ensuing mathematical difficulties are overcome by sharpening standard arguments.

MSC 2000:: *62M10 Time series, etc. (statistics)
62G07 Curve estimation
62J02 General nonlinear regression

Keywords: fixed design; martingale difference; linear time series; noisy observations; additive dependent noise; general linear process; discrete noise

Cited in: Zbl 1010.62085

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