ESTIMATING NONLINEAR STRUCTURAL RELATIONSHIPS

We consider the estimation of a general nonlinear structural relationship when the model is identifiable. In contrast to traditional approaches, the estimation method proposed does not require knowledge of the error variances provided that the model is identifiable. The model is effectively parametric in nature, but that the practitioner is not required to come up with a complete distributional formulation of the underlying latent variable. This is made possible using the general approximation to probability distributions given in Mak and Nebebe [13]. Since the proposed approach is likelihood based, the resulting estimators are approximately consistent and efficient. As a by-product, the entire distribution of the latent variable can be obtained and that a simple test for normality can also be easily derived.