  The least absolute shrinkage and selection operator (LASSO) is a popular
technique for simultaneous estimation and model selection. There have been a
lot of studies on the large sample asymptotic distributional properties of the
LASSO estimator, but it is also well-known that the asymptotic results can give
a wrong picture of the LASSO estimator's actual finite-sample behavior. The
finite sample distribution of the LASSO estimator has been previously studied
for the special case of orthogonal models. The aim in this work is to
generalize the finite sample distribution properties of LASSO estimator for a
real and linear measurement model in Gaussian noise.
  In this work, we derive an expression for the finite sample characteristic
function of the LASSO estimator, we then use the Fourier slice theorem to
obtain an approximate expression for the marginal probability density functions
of the one-dimensional components of a linear transformation of the LASSO
estimator.
