Approximating Symmetrized Estimators of Scatter via Balanced Incomplete U-Statistics

08/19/2022

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by   Lutz Duembgen, et al.

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We derive limiting distributions of symmetrized estimators of scatter, where instead of all n(n-1)/2 pairs of the n observations we only consider nd suitably chosen pairs, 1 ≤ d < ⌊ n/2⌋. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever 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,say, 10 and 20 yield already estimators which are computationally feasible and rather close to the original ones.