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Chen, Ziqi and Leng, Chenlei (2016) Dynamic covariance models. Journal of the American Statistical Association, 111 (515). pp. 1196-1207. doi:10.1080/01621459.2015.1077712
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Official URL: http://dx.doi.org/10.1080/01621459.2015.1077712
Abstract
An important problem in contemporary statistics is to understand the relationship among a large number of variables based on a dataset, usually with p, the number of the variables, much larger than n, the sample size. Recent efforts have focused on modeling static covariance matrices where pairwise covariances are considered invariant. In many
real systems, however, these pairwise relations often change. To characterize the changing correlations in a high dimensional system, we study a class of dynamic covariance models (DCMs) assumed to be sparse, and investigate for the first time a unified theory for understanding their non-asymptotic error rates and model selection properties. In particular, in the challenging high dimension regime, we highlight a new uniform consistency theory in which the sample size can be seen as n 4/5 when the bandwidth parameter is chosen as
h ∝ n −1/5 for accounting for the dynamics. We show that this result holds uniformly over a range of the variable used for modeling the dynamics. The convergence rate bears the mark of the familiar bias-variance trade-off in the kernel smoothing literature. We illustrate the
results with simulations and the analysis of a neuroimaging dataset.
Item Type: | Journal Item | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Analysis of covariance | ||||||||
Journal or Publication Title: | Journal of the American Statistical Association | ||||||||
Publisher: | American Statistical Association | ||||||||
ISSN: | 0162-1459 | ||||||||
Official Date: | 18 October 2016 | ||||||||
Dates: |
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Volume: | 111 | ||||||||
Number: | 515 | ||||||||
Number of Pages: | 43 | ||||||||
Page Range: | pp. 1196-1207 | ||||||||
DOI: | 10.1080/01621459.2015.1077712 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 28 July 2016 | ||||||||
Date of first compliant Open Access: | 8 February 2017 | ||||||||
Funder: | Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC) | ||||||||
Grant number: | 11401593 (NSFC), 20130162120086 (NSFC), 2013M531796 (NSFC), 2014T70778 (NSFC) | ||||||||
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