fastM-package

tools:::Rd_package_title("fastM")

tools:::Rd_package_description("fastM") package

Details

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.

Author(s)

tools:::Rd_package_author("fastM")

Maintainer: tools:::Rd_package_maintainer("fastM")

References

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

Duembgen, L., Nordhausen, K. and Schuhmacher, H. (2016), New algorithmsfor M-estimation of multivariate location and scatter, Journal ofMultivariate Analysis, 144, 200-217.\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmva.2015.11.009")}

Kent, J.T., Tyler, D.E. and Vardi, Y. (1994), A curious likelihoodidentity for the multivariate t-distribution, Communications inStatistics, Theory and Methods, 23, 441-453.

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