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Cluster-Seeking James–Stein Estimators.
- Source :
- IEEE Transactions on Information Theory; Feb2018, Vol. 64 Issue 2, p853-874, 22p
- Publication Year :
- 2018
-
Abstract
- This paper considers the problem of estimating a high-dimensional vector of parameters \theta \in \mathbb R^n from a noisy observation. The noise vector is independent identically distributed Gaussian with known variance. For a squared-error loss function, the James–Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector toward the origin, and the risk reduction over the ML-estimator is greatest for {\theta } that lie close to the origin. JS-estimators can be generalized to shrink the data toward any target subspace. Such estimators also dominate the ML-estimator, but the risk reduction is significant only when {\theta } lies close to the subspace. This leads to the question: in the absence of prior information about \theta , how do we design estimators that give significant risk reduction over the ML-estimator for a wide range of \theta ? In this paper, we propose shrinkage estimators that attempt to infer the structure of \theta from the observed data in order to construct a good attracting subspace. In particular, the components of the observed vector are separated into clusters, and the elements in each cluster shrunk toward a common attractor. The number of clusters and the attractor for each cluster are determined from the observed vector. We provide concentration results for the squared-error loss and convergence results for the risk of the proposed estimators. The results show that the estimators give significant risk reduction over the ML-estimator for a wide range of \theta , particularly for large $n$ . Simulation results are provided to support the theoretical claims. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 64
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 127409001
- Full Text :
- https://doi.org/10.1109/TIT.2017.2783543