  We consider the linear regression problem. We propose the S-Lasso procedure
to estimate the unknown regression parameters. This estimator enjoys sparsity
of the representation while taking into account correlation between successive
covariates (or predictors). The study covers the case when $p\gg n$, i.e. the
number of covariates is much larger than the number of observations. In the
theoretical point of view, for fixed $p$, we establish asymptotic normality and
consistency in variable selection results for our procedure. When $p\geq n$, we
provide variable selection consistency results and show that the S-Lasso
achieved a Sparsity Inequality, i.e., a bound in term of the number of non-zero
components of the oracle vector. It appears that the S-Lasso has nice variable
selection properties compared to its challengers. Furthermore, we provide an
estimator of the effective degree of freedom of the S-Lasso estimator. A
simulation study shows that the S-Lasso performs better than the Lasso as far
as variable selection is concerned especially when high correlations between
successive covariates exist. This procedure also appears to be a good
challenger to the Elastic-Net (Zou and Hastie, 2005).
