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#### UM E-Theses Collection (澳門大學電子學位論文庫)

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Title

Lasso and Dantzig selector for sparse linear system with strong mixing errors

English Abstract

In this thesis, the topic is concentrated on Lasso and Dantzig selector applied in a new linear model with α-mixing errors (or strong mixing). In particular, we focus on the case that the number of variables or parameters p is larger than the sample size n, even p n. Making a restricted eigenvalue assumption on the Gram matrix, i.e. Σ = b 1 nXT X, X ∈ R n×p , we obtain the bounds on the rate of convergence of Lasso and Dantzig selector under the sparsity scenario, i.e. when the number of non-zero components of the true parameters is small. The both bounds of kβb−β ∗k1 are O( qlog p n ), and that of 1 n kX(βb − β ∗ )k 2 2 are O( log p n ). For completeness, we give the approximate equivalent relation and the oracle inequalities for prediction loss. Our experiments show that the both methods do very well when p > n.

Issue date

2015

Author

Xie, Fang

Faculty

Faculty of Science and Technology

Degree

M.Sc.

Subject

Sparse matrices

Linear systems -- Mathematical models

Mathematics -- Department of Mathematics

Supervisor

Xu, Li Hu

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Location
1/F Zone C
Library URL
991000747159706306