UM ETheses Collection (澳門大學電子學位論文庫)
 Title

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

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In this thesis, the topic is concentrated on Lasso and Dantzig selector applied in a new linear model with αmixing 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 nonzero 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
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991000747159706306