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The Lasso estimator: distributional properties. (English) Zbl 1449.62162

Summary: 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 behaviour. 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.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62J05 Linear regression; mixed models
62G05 Nonparametric estimation
60E05 Probability distributions: general theory

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