On cross-validated Lasso

Denis Chetverikov and . .

No 47/16, CeMMAP working papers from Institute for Fiscal Studies

Abstract: In this paper, we derive a rate of convergence of the Lasso estimator when the penalty parameter λ for the estimator is chosen using K-fold cross-validation; in particular, we show that in the model with Gaussian noise and under fairly general assumptions on the candidate set of values of λ, the prediction norm of the estimation error of the cross-validated Lasso estimator is with high probability bounded from above up-to a constant by (s log p/n)1/2 (log7/8n) as long as p log n/n = o(1) and some other mild regularity conditions are satisfied where n is the sample size of available data, p is the number of covariates, and s is the number of non-zero coefficients in the model. Thus, the cross-validated Lasso estimator achieves the fastest possible rate of convergence up-to the logarithmic factor log7/8 n. In addition, we derive a sparsity bound for the cross-validated Lasso estimator; in particular, we show that under the same conditions as above, the number of non-zero coefficients of the estimator is with high probability bounded from above up-to a constant by s log5 n. Finally, we show that our proof technique generates non-trivial bounds on the prediction norm of the estimation error of the cross-validated Lasso estimator even if p is much larger than n and the assumption of Gaussian noise fails; in particular, the prediction norm of the estimation error is with high-probability bounded from above up-to a constant by (s log2(pn) / n)1/4 under mild regularity conditions.

Date: 2016-09-27
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.cemmap.ac.uk/wp-content/uploads/2020/08/CWP4716.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:azt:cemmap:47/16

DOI: 10.1920/wp.cem.2016.4716

Access Statistics for this paper

More papers in CeMMAP working papers from Institute for Fiscal Studies Contact information at EDIRC.
Bibliographic data for series maintained by Dermot Watson ().