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.