Date of Award
2012
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Statistics
First Advisor
Andreas Buja
Second Advisor
Zongming Ma
Abstract
Singular value decomposition is a widely used tool for dimension reduction in multivariate analysis. However, when used for statistical estimation in high-dimensional low rank matrix models, singular vectors of the noise-corrupted matrix are inconsistent for their counterparts of the true mean matrix. We suppose the true singular vectors have sparse representations in a certain basis. We propose an iterative thresholding algorithm that can estimate the subspaces spanned by leading left and right singular vectors and also the true mean matrix optimally under Gaussian assumption. We further turn the algorithm into a practical methodology that is fast, data-driven and robust to heavy-tailed noises. Simulations and a real data example further show its competitive performance. The dissertation contains two chapters. For the ease of the delivery, Chapter 1 is dedicated to the description and the study of the practical methodology and Chapter 2 states and proves the theoretical property of the algorithm under Gaussian noise.
Recommended Citation
Yang, Dan, "Singular Value Decomposition for High Dimensional Data" (2012). Publicly Accessible Penn Dissertations. 595.
https://repository.upenn.edu/edissertations/595