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Abstract:
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The Lasso estimator is a commonly used regression method for high-dimensional regression models in which the number of covariates $p$ is larger than the number of observations $n$. It is known that in the regime where the ratio $n/p$ is a constant, the Lasso estimator has a non-trivial distribution that involves extra noise due to the under-sampling effect. In this work, we first characterize the exact distribution of the Lasso estimator for a general class of design matrices with arbitrary covariance structure. This exact characterization enables us to develop some interesting consequences in risk estimation, hypothesis testing, and model selection.
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