Second-order accuracy of depth-based bootstrap confidence regions

Bei Wei and Stephen M.S. Lee

Journal of Multivariate Analysis, 2012, vol. 105, issue 1, 112-123

Abstract: We consider the problem of setting bootstrap confidence regions for multivariate parameters based on data depth functions. We prove, under mild regularity conditions, that depth-based bootstrap confidence regions are second-order accurate in the sense that their coverage error is of order n−1, given a random sample of size n. The results hold in general for depth functions of types A and D, which cover as special cases the Tukey depth, the majority depth, and the simplicial depth. A simulation study is also provided to investigate empirically the bootstrap confidence regions constructed using these three depth functions.

Keywords: Confidence region; Depth function; Second-order accurate (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.jmva.2011.08.016

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