  The Least Absolute Shrinkage and Selection Operator (LASSO) has gained
attention in a wide class of continuous parametric estimation problems with
promising results. It has been a subject of research for more than a decade.
Due to the nature of LASSO, the previous analyses have been non-parametric.
This ignores useful information and makes it difficult to compare LASSO to
traditional estimators. In particular, the role of the regularization parameter
and super-resolution properties of LASSO have not been well-understood yet. The
objective of this work is to provide a new insight into this context by
introducing LASSO as a parametric technique of a varying order. This provides
us theoretical expressions for the LASSO-based estimation error and false alarm
rate in the asymptotic case of high SNR and dense grids. For this case, LASSO
is compared to maximum likelihood and conventional beamforming. It is found
that LASSO loses performance due to the regularization term, but the amount of
loss is practically negligible with a proper choice of the regularization
parameter. Thus, we provide suggestions on the selection of the regularization
parameter. Without loss of generality, we present the comparative numerical
results in the context of Direction of Arrival (DOA) estimation using a sensor
array.
