M-estimation in a multivariate regression model under a convex-contoured discrepancy function

Abstract

The M-estimation in a multivariate regression model is studied in this paper using a convex-contoured discrepancy function (C-CDF). Most of the discrepancy functions considered by various authors can be expressed as C-CDF's. A general asymptotic theory of M-estimation is developed that includes strong consistency, asymptotic representation and asymptotic normality. Results of this paper generalize most of the results in the literature on M-estimation under a minimal set of assumptions.