Multivariate regression estimates based on ranks and generalized ranks are proposed. These estimates are based on a transformation and retransformation technique that uses Tyler’s (1987) M-estimator of scatter. The proposed estimates are obtained by retransforming the componentwise rank-based estimate due to Davis and McKean (1993) and a componentwise generalized rank estimate. Asymptotic properties of the estimates are established under some regularity conditions. It is shown that both estimates have a multivariate normal limiting distribution. The influence function of the retransformed generalized rank estimate has a bounded influence in both factor and response spaces. It is shown through a simulation study that the transformed-retransformed R and GR estimates are highly efficient compared to the componentwise R, GR and least absolute deviations estimates. Also, it is shown that the new estimates perform better than the least squares estimate when the errors have a heavy tailed distribution. An example illustrating the estimation procedures is presented.
Digital Object Identifier (DOI)
Salman, Majeda and W. McKean, Joseph
"On Multivariate Rank and Generalized Rank Regression,"
Journal of Statistics Applications & Probability: Vol. 2
, Article 1.
Available at: https://dc.naturalspublishing.com/jsap/vol2/iss2/1