Pivotal estimation via square-root lasso in nonparametric regression

Alexandre Belloni, Victor Chernozhukov and Lie Wang
Additional contact information
Alexandre Belloni: Institute for Fiscal Studies
Lie Wang: Institute for Fiscal Studies

No CWP62/13, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: We propose a self-tuning v Lasso method that simultaneiously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity, and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example perfectly collinear regressors, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case, in contrast to Lasso. We establish various non-asymptotic bounds for v Lasso including prediction norm rate and sharp sparcity bound. Our analysis is based on new impact factors that are tailored to establish prediction rates. In order to cover heteroscedastic non-Gaussian noise, we rely on moderate deviation theory for self-normalized sums to achieve Gaussian-like results under weak conditions. Moreover, we derive bounds on the performance of ordinary least square (ols) applied to the model selected by v Lasso accounting for possible misspecification of the selected model. Under mild conditions the rate of convergence of ols post v Lasso is no worse than v Lasso even with a misspecified selected model and possibly better otherwise. As an application, we consider the use of v Lasso and post v Lasso as estimators of nuisance parameters in a generic semi-parametric problem (nonlinear instrumental/moment condition or Z-estimation problem).

Date: 2013-12-10
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.cemmap.ac.uk/wps/cwp621313.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Working Paper: Pivotal estimation via square-root lasso in nonparametric regression (2013)
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:ifs:cemmap:62/13

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().