Two-stage regression quantiles and two-stage trimmed least squares estimators for structural equation models

Abstract

We propose a two-stage trimmed least squares estimator for the parameters of structural equation model and provide the corresponding asymptotic distribution theory. The estimator is based on two-stage regression quantiles, which generalize the standard Linear model regression quantiles introduced by Koenker and Bassett (1978). The asymptotic theory is developed by means of ''Barhadur'' representations for the two-stage regression quantiles and the two-stage trimmed least squares estimator. The representations approximate these estimators as sums of independent random variables plus an additive term involving the first stage estimator. Asymptotic normal distributions are derived from these representations, and a simulation comparing some two-stage estimators is presented.