Detection of Signal in the Spiked Rectangular Models

• URL: http://arxiv.org/abs/2104.13517v1
• Date: Wed, 28 Apr 2021 01:15:45 GMT
• Title: Detection of Signal in the Spiked Rectangular Models
• Authors: Ji Hyung Jung, Hye Won Chung, Ji Oon Lee
• Abstract summary: We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. We also propose a hypothesis test to detect the presence of signal with low computational complexity.
• Score: 8.185918509343818
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik-Ben Arous-P\'ech\'e (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.

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