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Local linear estimation of covariance matrices via Cholesky decomposition
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Chen, Ziqi and Leng, Chenlei (2015) Local linear estimation of covariance matrices via Cholesky decomposition. Statistica Sinica, 25 . pp. 1249-1263. doi:10.5705/ss.2013.129 ISSN 1017-0405.
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Official URL: http://dx.doi.org/10.5705/ss.2013.129
Abstract
A fundamental problem in multivariate statistics is the estimation of covariance matrices. We consider in this paper a flexible class of nonparametric covariance models for which the entries in the covariance matrix depend on covariates. Although it is well known that local linear estimation is much preferred over local constant estimation (Fan & Gijbels, 1996), developing the former for estimating covariance matrices is challenging due to the positive definiteness constraint of such matrices. Motivated by the modified Cholesky decomposition, we propose for the first time a local linear estimator of the nonparametric covariance matrix. The proposed estimator is positive definite, is adaptive, possesses good theoretical properties and performs well in numerical studies. An application to the Boston housing data is also provided to illustrate attractive finite-sample performance of the proposed method.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Statistica Sinica | ||||||
Publisher: | Academia Sinica * Institute of Statistical Science | ||||||
ISSN: | 1017-0405 | ||||||
Official Date: | 2015 | ||||||
Dates: |
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Volume: | 25 | ||||||
Page Range: | pp. 1249-1263 | ||||||
DOI: | 10.5705/ss.2013.129 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 29 September 2017 |
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