Approximating symmetrized estimators of scatter via balanced incomplete U-statistics

Lutz Dümbgen () and Klaus Nordhausen
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Lutz Dümbgen: University of Bern
Klaus Nordhausen: University of Jyväskylä

Annals of the Institute of Statistical Mathematics, 2024, vol. 76, issue 2, No 1, 185-207

Abstract: Abstract We derive limiting distributions of symmetrized estimators of scatter. Instead of considering all $$n(n-1)/2$$ n ( n - 1 ) / 2 pairs of the n observations, we only use nd suitably chosen pairs, where $$d \ge 1$$ d ≥ 1 is substantially smaller than n. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever $$d = d(n) \rightarrow \infty$$ d = d ( n ) → ∞ at arbitrarily slow speed. We also investigate the asymptotic properties for arbitrary fixed d. These considerations and numerical examples indicate that for practical purposes, moderate fixed values of d between 10 and 20 yield already estimators which are computationally feasible and rather close to the original ones.

Keywords: Asymptotic normality; Incomplete U-statistic; Independent component analysis; Linear expansion; U-statistic (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10463-023-00879-1

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