Nonparametric estimation of a log-variance function in scale-space

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In a nonparametric regression setting, we consider the kernel estimation of the logarithm of the error variance function, which might be assumed to be homogeneous or heterogeneous. The objective of the present study is to discover important features in the variation of the data at multiple locations and scales based on a nonparametric kernel smoothing technique. Traditional kernel approaches estimate the function by selecting an optimal bandwidth, but it often turns out to be unsatisfying in practice. In this paper, we develop a SiZer (Significant ZERo crossings of derivatives) tool based on a scale-space approach that provides a more flexible way of finding meaningful features in the variation. The proposed approach utilizes local polynomial estimators of a log-variance function using a wide range of bandwidths. We derive the theoretical quantile of confidence intervals in SiZer inference and also study the asymptotic properties of the proposed approach in scale-space. A numerical study via simulated and real examples demonstrates the usefulness of the proposed SiZer tool. (C) 2013 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2013-10
Language
English
Article Type
Article
Citation

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, v.143, no.10, pp.1766 - 1780

ISSN
0378-3758
DOI
10.1016/j.jspi.2013.06.004
URI
http://hdl.handle.net/10203/285758
Appears in Collection
MA-Journal Papers(저널논문)
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