Choice of estimation of unknown parameter under contaminated error model
(College of Resource; Environment and Civil Engineering; Central South University of Technology; Changsha 410083; P. R. China)
Abstract: The ε -contaminated normal distribution, ψ(Δ ) = (1 - ε )ψ0(Δ ) +εψ1 (Δ ), was considered as error model occurring in practice (ψ = probability function, Δ = observation error). The variances of the L1 (Least Absolute Sum) estimation and the L2 (Least Squares) estimation were compared with each other based on their asymptotic distribution. The revised L2 estimation was then derived. The conditions that the L1 estimation is superior to the L2 estimation and that the revised L2 estimation is superior to L1 estimation were discussed.
Key words: contaminated model; least squares estimation; least absolute sum estimation