Eigenvalues in multivariate random effects models
- Zhou Fan.
- [Stanford, California] : [Stanford University], 2018.
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- 1 online resource.
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|3781 2018 F||In-library use|
- We study principal component analyses in multivariate random and mixed effects linear models. These models are commonly used in quantitative genetics to decompose the variation of phenotypic traits into consistuent variance components. Applications arising in evolutionary biology require understanding the eigenvalues and eigenvectors of these components in high-dimensional multivariate settings. However, these quantities may be difficult to estimate from limited samples when the number of traits is large. We describe several phenomena concerning sample eigenvalues and eigenvectors of classical MANOVA estimators in the presence of high-dimensional noise, including dispersion of the bulk eigenvalue distribution, bias and aliasing of outlier eigenvalues and eigenvectors, and Tracy-Widom fluctuations at the spectral edges. A common theme is that the spectral properties of the MANOVA estimate for one component may be influenced by the other components. In the setting of a simple spiked covariance model, we introduce alternative estimators for the leading eigenvalues and eigenvectors that correct for this problem in a high-dimensional asymptotic regime.
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- Submitted to the Department of Statistics.
- Thesis Ph.D. Stanford University 2018.
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