Choice of estimation of unknown parameter under contaminated error model

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.

The epsilon -contaminated normal distribution, psi(Delta) = (1 - epsilon)psi(0)(Delta) + epsilon psi(1)(Delta), was considered as error model occurring in practice ( psi = probability function, Delta = observation error). The variances of the L-1 (Least Absolute Sum) estimation and the L-2 (Least Squares) estimation were compared with each other based on their asymptotic distribution. The revised L-2 estimation was then derived. The conditions that the L-1 estimation is superior to the L-2 estimation and that the revised L-2 estimation is superior to L-1 estimation were discussed.