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B. Pötscher, U. Schneider:
"Distributional Results for Thresholding Estimators in High-Dimensional Gaussian Regression Models";
Vortrag: 29th European Meeting of Statisticians, Budapest, Ungarn; 20.07.2013 - 25.07.2013.

We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear
regression model where the number of parameters k can depend on sample size n and may diverge
with n. In addition to the case of known error-variance, we define and study versions of the estimators
when the error-variance is unknown. We derive the finite-sample distribution of each estimator
and study its behavior in the large-sample limit, also investigating the effects of having to estimate
the variance when the degrees of freedom n 􀀀 k does not tend to infinity or tends to infinity very
slowly. Our analysis encompasses both the case where the estimators are tuned to perform consistent
model selection and the case where the estimators are tuned to perform conservative model
selection. Furthermore, we discuss consistency, uniform consistency and derive the minimax rate
under either type of tuning.
Acknowledgment. This research was partially supported by the Deutsche Forschungsgemeinschaft project
FOR916.