Rate Optimal Estimation for High Dimensional Spatial Covariance Matrices

Yi Li, Aidong Adam Ding, Jennifer Dy
Proceedings of the Ninth Asian Conference on Machine Learning, PMLR 77:208-223, 2017.

Abstract

Spatial covariance matrix estimation is of great significance in many applications in climatology, econometrics and many other fields with complex data structures involving spatial dependencies. High dimensionality brings new challenges to this problem, and no theoretical optimal estimator has been proved for the spatial high-dimensional covariance matrix. Over the past decade, the method of regularization has been introduced to high-dimensional covariance estimation for various structured matrices, to achieve rate optimal estimators. In this paper, we aim to bridge the gap in these two research areas. We use a structure of block bandable covariance matrices to incorporate spatial dependence information, and study rate optimal estimation of this type of structured high dimensional covariance matrices. A double tapering estimator is proposed, and is shown to achieve the asymptotic minimax error bound. Numerical studies on both synthetic and real data are conducted showing the improvement of the double tapering estimator over the sample covariance matrix estimator.

Cite this Paper

BibTeX
@InProceedings{pmlr-v77-li17a, title = {Rate Optimal Estimation for High Dimensional Spatial Covariance Matrices}, author = {Li, Yi and Ding, Aidong Adam and Dy, Jennifer}, booktitle = {Proceedings of the Ninth Asian Conference on Machine Learning}, pages = {208--223}, year = {2017}, editor = {Zhang, Min-Ling and Noh, Yung-Kyun}, volume = {77}, series = {Proceedings of Machine Learning Research}, address = {Yonsei University, Seoul, Republic of Korea}, month = {15--17 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v77/li17a/li17a.pdf}, url = {https://proceedings.mlr.press/v77/li17a.html}, abstract = {Spatial covariance matrix estimation is of great significance in many applications in climatology, econometrics and many other fields with complex data structures involving spatial dependencies. High dimensionality brings new challenges to this problem, and no theoretical optimal estimator has been proved for the spatial high-dimensional covariance matrix. Over the past decade, the method of regularization has been introduced to high-dimensional covariance estimation for various structured matrices, to achieve rate optimal estimators. In this paper, we aim to bridge the gap in these two research areas. We use a structure of block bandable covariance matrices to incorporate spatial dependence information, and study rate optimal estimation of this type of structured high dimensional covariance matrices. A double tapering estimator is proposed, and is shown to achieve the asymptotic minimax error bound. Numerical studies on both synthetic and real data are conducted showing the improvement of the double tapering estimator over the sample covariance matrix estimator.} }
Endnote
%0 Conference Paper %T Rate Optimal Estimation for High Dimensional Spatial Covariance Matrices %A Yi Li %A Aidong Adam Ding %A Jennifer Dy %B Proceedings of the Ninth Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Min-Ling Zhang %E Yung-Kyun Noh %F pmlr-v77-li17a %I PMLR %P 208--223 %U https://proceedings.mlr.press/v77/li17a.html %V 77 %X Spatial covariance matrix estimation is of great significance in many applications in climatology, econometrics and many other fields with complex data structures involving spatial dependencies. High dimensionality brings new challenges to this problem, and no theoretical optimal estimator has been proved for the spatial high-dimensional covariance matrix. Over the past decade, the method of regularization has been introduced to high-dimensional covariance estimation for various structured matrices, to achieve rate optimal estimators. In this paper, we aim to bridge the gap in these two research areas. We use a structure of block bandable covariance matrices to incorporate spatial dependence information, and study rate optimal estimation of this type of structured high dimensional covariance matrices. A double tapering estimator is proposed, and is shown to achieve the asymptotic minimax error bound. Numerical studies on both synthetic and real data are conducted showing the improvement of the double tapering estimator over the sample covariance matrix estimator.
APA
Li, Y., Ding, A.A. & Dy, J.. (2017). Rate Optimal Estimation for High Dimensional Spatial Covariance Matrices. Proceedings of the Ninth Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 77:208-223 Available from https://proceedings.mlr.press/v77/li17a.html.

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