Nonparametric estimation of ratios of noise to signal in stochastic regression

Tong, Howell and Yao, Qiwei ORCID: 0000-0003-2065-8486 (2000) Nonparametric estimation of ratios of noise to signal in stochastic regression. Statistica Sinica, 10 (3). pp. 751-770. ISSN 1017-0405

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Abstract

In this paper, we study three different types of estimates for the noise-to signal ratios in a general stochastic regression setup. The locally linear and locally quadratic regression estimators serve as the building blocks in our approach. Under the assumption that the observations are strictly stationary and absolutely regular, we establish the asymptotic normality of the estimates, which indicates that the residual-based estimates are to be preferred. Further, the locally quadratic regression reduces the bias when compared with the locally linear (or locally constant) regression without the concomitant increase in the asymptotic variance, if the same bandwidth is used. The asymptotic theory also paves the way for a fully data-driven under smoothing scheme to reduce the biases in estimation. Numerical examples with both simulated and real data sets are used as illustration.

Item Type:	Article
Official URL:	http://www3.stat.sinica.edu.tw/statistica/
Additional Information:	© 2000 Academia Sinica
Divisions:	Economics Statistics
Subjects:	H Social Sciences > H Social Sciences (General) H Social Sciences > HA Statistics
Date Deposited:	07 Jul 2008 13:45
Last Modified:	01 Oct 2024 03:30
Projects:	L16358
Funders:	Engineering and Physical Sciences Research Council
URI:	http://eprints.lse.ac.uk/id/eprint/6324

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