, Volume 74, Issue 1, pp 10-28

A note on the asymptotic distribution of LASSO estimator for correlated data

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Abstract

The asymptotic distribution of the Lasso estimator for regression models with independent errors has been investigated by Knight and Fu (2000). In this note we extend these results to regression models with a general weak dependence structure. We determine the asymptotic distribution of the Lasso estimator when the number of parameters M is fixed and the number of observations, n, converges to infinity. We show that, for an appropriate choice of the tuning parameter of the method, this asymptotic distribution reduces to a multivariate normal distribution. As an illustrative example, the special case of AR(1) is also investigated.