Sparse Signal Recovery with Subbotin Noise
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In this thesis, we expand upon the work of Cui [4] and earlier authors by studying the problem of variable selection in a high-dimensional setting. Specifically, we consider a single vector X from a sequence model with noise components originating from a generalized normal distribution and determine the regions of exact and almost full selection with respect to a Hamming loss function. We make the routine assumption that the model studied is sparse. That is, the informative number of components is tiny in the model relative to the dimension d. An adaptive procedure is also proposed for estimating the signal components of X when the level of sparsity is unknown. A synthetic simulation and empirical study is then presented to showcase the aforementioned results. Lastly, we conclude the thesis by proposing areas of future work.
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Copyright © 2022 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 2022
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miller-sparsesignalrecoverywithsubbotinnoise.pdf | 2023-05-05 | Public | Download |