Estimation of an unstructured covariance matrix is difficult because of its positive-definiteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying-coefficient and varying-order regression models. Our framework is similar to the use of increasing-order autoregressive models in approximating the covariance matrix or the spectrum of a stationary time series. As an illustration, we adopt Fan & Zhang's (2000) two-step estimation of functional linear models and propose nonparametric estimators of covariance matrices which are guaranteed to be positive definite. For parsimony a suitable order for the sequence of (auto)regression models is found using penalised likelihood criteria like AIC and BIC. Some asymptotic results for the local polynomial estimators of components of a covariance matrix are established. Two longitudinal datasets are analysed to illustrate the methodology. A simulation study reveals the advantage of the nonparametric covariance estimator over the sample covariance matrix for large covariance matrices. Copyright Biometrika Trust 2003, Oxford University Press.
Download Info
To our knowledge, this item is not available for
download. To find whether it is available, there are three
options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page
whether it is in fact available.
3. Perform a search for a similarly titled item that would be
available.
Publisher Info
Article provided by Oxford University Press for Biometrika Trust in its journal Biometrika.
Volume (Year): 90 (2003) Issue (Month): 4 (December) Pages: 831-844 Download reference. The following formats are available: HTML
(with abstract),
plain text
(with abstract),
BibTeX,
RIS (EndNote, RefMan, ProCite),
ReDIF
Contact details of provider: Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK Fax: 01865 267 985 Email: Web page: http://biomet.oxfordjournals.org/
For technical questions regarding this item, or to correct its listing, contact: (Christopher F. Baum).
Related research
Keywords:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)