Central limit theorems and bootstrap in high dimensions

Victor Chernozhukov, Denis Chetverikov () and Kengo Kato
Additional contact information
Denis Chetverikov: Institute for Fiscal Studies and UCLA
Kengo Kato: Institute for Fiscal Studies

No CWP39/16, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: In this paper, we derive central limit and bootstrap theorems for probabilities that centered high-dimensional vector sums hit rectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for the probabilities that a root-n rescaled sample average of Xi is in A, where X1,..., Xnare independent random vectors in Rp and A is a rectangle, or, more generally, a sparsely convex set, and show that the approximation error converges to zero even if p=pn-> infinity and p>>n; in particular, p can be as large as O(e^(Cn^c)) for some constants c,C>0. The result holds uniformly over all rectangles, or more generally, sparsely convex sets, and does not require any restrictions on the correlation among components of Xi. Sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend nontrivially only on a small subset of their arguments, with rectangles being a special case.

Keywords: Central limit theorem; bootstrap limit theorems; high dimensions; hyperrectangles; sparsely convex sets. (search for similar items in EconPapers)
Date: 2016-08-26
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.ifs.org.uk/uploads/cemmap/wps/cwp391616.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.ifs.org.uk/uploads/cemmap/wps/cwp391616.pdf [302 Found]--> https://ifs.org.uk/uploads/cemmap/wps/cwp391616.pdf)

Related works:
Working Paper: Central limit theorems and bootstrap in high dimensions (2016)
Working Paper: Central limit theorems and bootstrap in high dimensions (2014)
Working Paper: Central limit theorems and bootstrap in high dimensions (2014)
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:39/16

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 ().