Depth weighted scatter estimators

Details Depth weighted scatter estimators Depth weighted scatter estimators

2005-04-25

arxiv.org/abs/math/0504514v1

Annals of Statistics 2005, Vol. 33, No. 1, 381-413

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000922 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000922

General depth weighted scatter estimators are introduced and investigated. For general depth functions, we find out that these affine equivariant scatter estimators are Fisher consistent and unbiased for a wide range of multivariate distributions, and show that the sample scatter estimators are strong and \sqrtn-consistent and asymptotically normal, and the influence functions of the estimators exist and are bounded in general. We then concentrate on a specific case of the general depth weighted scatter estimators, the projection depth weighted scatter estimators, which include as a special case the well-known Stahel-Donoho scatter estimator whose limiting distribution has long been open until this paper. Large sample behavior, including consistency and asymptotic normality, and efficiency and finite sample behavior, including breakdown point and relative efficiency of the sample projection depth weighted scatter estimators, are thoroughly investigated. The influence function and the maximum bias of the projection depth weighted scatter estimators are derived and examined. Unlike typical high-breakdown competitors, the projection depth weighted scatter estimators can integrate high breakdown point and high efficiency while enjoying a bounded-influence function and a moderate maximum bias curve. Comparisons with leading estimators on asymptotic relative efficiency and gross error sensitivity reveal that the projection depth weighted scatter estimators behave very well overall and, consequently, represent very favorable choices of affine equivariant multivariate scatter estimators.

Affiliated with

Also associated with

No associations

Rating

Depth weighted scatter estimators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Depth weighted scatter estimators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Depth weighted scatter estimators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-468941