U-Estimators of Regression Coefficients

For the regression model yi = x′iξ + ei, 1 ≤ i ≤ n, with i.i.d. residuals {ei}, we introduce the estimator of ξ which zeros the weighted U-statistic ∑∑ qijK(êi, êj), where qij is a score vector for regression vectors xi and xj. These include some M- and R-estimators. Asymptotic inference is developed without the need to estimate the (ƒ′/ƒ) function, where ƒ is the pdf of the residuals.