Description Details Author(s) References

Implements the new algorithm for fast computation of M-scatter matrices using a partial Newton-Raphson procedure for several estimators. The algorithm is described in Duembgen, Nordhausen and Schuhmacher (2016) <doi:10.1016/j.jmva.2015.11.009>.

Multivariate M-estimators are usually computed using a fixed-point algorithm. As shown in Duembgen et al. (2016) a partial Newton-Raphson procedure applied to the second order Taylor expansion of the target function can make the computation considerably faster. We implement this new algorithm for the multivariate M-estimator of location and scatter using weights coming from the multivariate t-distribution (Kent et al., 1994), its symmetrized version, Tyler's shape matrix (Tyler, 1987) and Duembgen's shape matrix (Duembgen, 1998). For the symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.

Lutz Duembgen, Klaus Nordhausen, Heike Schuhmacher

Maintainer: Klaus Nordhausen <[email protected]>

Duembgen, L. (1998), On Tyler's M-functional of scatter in high dimension, *Annals of Institute of Statistical Mathematics*, **50**, 471–491.

Duembgen, L., Nordhausen, K. and Schuhmacher, H. (2016), New algorithms for M-estimation of multivariate location and scatter, *Journal of Multivariate Analysis*, **144**, 200–217. doi: 10.1016/j.jmva.2015.11.009

Kent, J.T., Tyler, D.E. and Vardi, Y. (1994), A curious likelihood identity for the multivariate t-distribution, *Communications in Statistics, Theory and Methods*, **23**, 441–453.

Tyler, D.E. (1987), A distribution-free M-estimator of scatter, *Annals of Statistics*, **15**, 234–251.

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