Please use this identifier to cite or link to this item:
Chernozhukov, Victor
Chetverikov, Denis
Kato, Kengo
Year of Publication: 
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP49/14
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(eCn)) 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.
Central limit theorem
bootstrap limit theorems
high dimensions
sparsely convex sets
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
633.41 kB

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.