Consistency of M-Estimates in General Regression Models

This paper extends the results of Chen and Wu [1] concerning consistency of M-estimators in the linear regression model. We consider M-estimators defined by [formula] in the general regression model yi = f(xi,θ ) + ϵi, where f(x, θ) is continuous on a separable metric space X ⊗ Θ, (x1, x2, ... ) is a deterministic design of experiment, and (ϵ1, ϵ2, ... ) are independet errors. This model has been considered previously by Richardson and Bhattacharyya [9], but they were restricted to ρ(x) = and their method differs from ours.