Asymptotics of generalized M-estimation of regression and scale with fixed carriers, in an approximately linear model

For the approximately linear model , with i.i.d. errors [epsilon]i and fixed carriers z(xi), we establish the asymptotic normality of a generalized M-estimator of regression/scale. The estimator minimizes a weighted Huber-Dutter loss function. The function fn(x) contributes a bias term to the asymptotic normal distribution; apart from this term the estimator is [radical sign]n-equivalent to the estimator obtained assuming the response to be exactly linear. Several estimate/design combinations are compared, in a simulation study.