Arbeitspapier

Central limit theorems and bootstrap in high dimensions

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,..., Xn are 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.

Sprache
Englisch

Erschienen in
Series: cemmap working paper ; No. CWP49/14

Klassifikation
Wirtschaft
Thema
Central limit theorem
bootstrap limit theorems
high dimensions
rectangles
sparsely convex sets

Ereignis
Geistige Schöpfung
(wer)
Chernozhukov, Victor
Chetverikov, Denis
Kato, Kengo
Ereignis
Veröffentlichung
(wer)
Centre for Microdata Methods and Practice (cemmap)
(wo)
London
(wann)
2014

DOI
doi:10.1920/wp.cem.2014.4914
Handle
Letzte Aktualisierung
10.03.2025, 11:43 MEZ

Datenpartner

Dieses Objekt wird bereitgestellt von:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.

Objekttyp

  • Arbeitspapier

Beteiligte

  • Chernozhukov, Victor
  • Chetverikov, Denis
  • Kato, Kengo
  • Centre for Microdata Methods and Practice (cemmap)

Entstanden

  • 2014

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