Core Concepts
Deploying the James-Stein shrinkage estimator in place of the maximum likelihood estimator can significantly improve the performance of quickest change detection procedures in multiple Gaussian data streams, especially when the number of streams is large.
Abstract
The paper studies the problem of quickest change detection in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams.
Key highlights:
- The authors propose using the James-Stein shrinkage estimator in place of the maximum likelihood estimator in existing change detection tests, such as the windowed CuSum (WL-CuSum) test and the Shiryaev-Roberts-Robbins-Siegmund (SRRS) test.
- For the WL-CuSum test, the authors show that the James-Stein version (JS-WL-CuSum) achieves a smaller detection delay simultaneously for all possible post-change parameter values and every false alarm rate constraint, as long as the number of parallel data streams is greater than three.
- For the SRRS test, the authors show that the James-Stein version (JS-SRRS) is second-order asymptotically minimax and superior to existing procedures like the GLR-CuSum test. The second-order detection delay term of the JS-SRRS test is shown to be independent of the number of streams in a prespecified lower dimensional subspace of the parameter space.
- Simulation experiments verify the analytical results and demonstrate that the proposed JS-WL-CuSum and JS-SRRS tests perform favorably compared to their maximum likelihood counterparts and the GLR-CuSum test, especially when the number of data streams is moderate to large.
Stats
The number of parallel data streams K is a key parameter in the problem formulation.
Quotes
"The James-Stein estimator dominates the maximum likelihood estimator in terms of mean square error (MSE) when estimating the mean of a multivariate Gaussian distribution when K ≥3."
"Utilizing the James-Stein estimator can reduce the second-order delay term in a predefined low-dimensional subspace of the post-change parameter space while simultaneously maintaining second-order asymptotic minimaxity."