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Asymptotic expansion of S‐estimators of location and covariance

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  • H. P. Lopuhaä

Abstract

By means of a straightforward application of empirical process theory, we show that S‐estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent vector and matrix valued random elements respectively. This provides an alternative proof of asymptotic normality of S‐estimators and clearly explains the limiting covariance structure. It also leads to a relatively simple proof of asymptotic normality of the length of the shortest α‐fraction.

Suggested Citation

  • H. P. Lopuhaä, 1997. "Asymptotic expansion of S‐estimators of location and covariance," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(2), pages 220-237, July.
    • Handle: RePEc:bla:stanee:v:51:y:1997:i:2:p:220-237
    DOI: 10.1111/1467-9574.00051
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