Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11029714 | Journal of Multivariate Analysis | 2019 | 13 Pages |
Abstract
The covariance operator plays an important role in modern statistical methods and is critical for inference. It is most often estimated by the empirical covariance operator. In spite of its simple and appealing properties, however, this estimator can be improved by a class of shrinkage operators. In this paper, we study shrinkage estimation of the covariance operator in reproducing kernel Hilbert spaces. A data-driven shrinkage estimator enjoying desirable theoretical and computational properties is proposed. The procedure is easily implemented and its numerical performance is investigated through simulations. In finite samples, the estimator outperforms the empirical covariance operator, especially when the data dimension is much larger than the sample size. We also show that the rate of convergence in Hilbert-Schmidt norm is of the order nâ1â2. Furthermore, we establish the minimax optimal rate of convergence over suitable classes of probability measures and demonstrate that these shrinkage operators are all minimax rate-optimal.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Yang Zhou, Di-Rong Chen, Wei Huang,