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Activity Number:
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519
- SPEED: Methodological Advances in Time Series: BandE Speed Session, Part 2
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Type:
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Contributed
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Date/Time:
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Wednesday, July 31, 2019 : 10:30 AM to 11:15 AM
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Sponsor:
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Business and Economic Statistics Section
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Abstract #307890
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Title:
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Testing Simultaneous Diagonalizability of Rrandom Matrices
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Author(s):
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Yuchen Xu* and David Matteson
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Companies:
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Cornell University and Cornell University
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Keywords:
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common eigenvectors;
simultaneous diagonalization;
joint diagonalization;
random matrix;
time series;
hypothesis test
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Abstract:
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Simultaneous diagonalization of random matrices is of great importance in statistical analysis. It can be used to decouple multivariate time series into several univariate time series, and to perform independent component analysis (ICA) on covariance matrices. We design hypothesis testing algorithms to check whether random matrices can be diagonalized simultaneously. Start with the two-sample case, we invent and analyze two tests of the null hypothesis that two matrices are jointly diagonalizable. One test is based on the Frobenius norm of their commutator, while the other is a likelihood ratio test. We generalize the two-sample tests to accommodate multi-sample settings by conducting pairwise tests on a pool of samples. We also introduce a new test concerning a given matrix as if it were consisted of the samples’ common eigenvectors. Numerical methods for pooled estimation of common eigenvectors are also studied. Theoretical derivations and numerical simulations demonstrate favorable performance of both tests.
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Authors who are presenting talks have a * after their name.
