Distributional results for thresholding estimators in high-dimensional Gaussian regression models
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.
|Date of creation:||Jun 2011|
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- Hannes Leeb & Benedikt M. Poetscher, 2005.
"Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator,"
Cowles Foundation Discussion Papers
1500, Cowles Foundation for Research in Economics, Yale University, revised Apr 2007.
- Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
- Leeb, Hannes & P tscher, Benedikt M., 2003.
"The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations,"
Cambridge University Press, vol. 19(01), pages 100-142, February.
- Hannes Leeb & Benedikt M. Poetscher, 2000. "The Finite-Sample Distribution of Post-Model-Selection Estimators, and Uniform Versus Non-Uniform Approximations," Econometrics 0004001, EconWPA.
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