## Nonlinear Limited Information Maximum Likelihood Estimator

In the preceding section we assumed the model (8.1.1) without specifying the model for Y( or assuming the normality of u, and derived the asymptotic distribution of the class of NL2S estimators and the optimal member of the class—BNL2S. In this section we shall specify the model for Y, and shall assume that all the error terms are normally distributed; under these assumptions we shall derive the nonlinear limited information maximum likelihood (NLLI) estimator, which is asymptotically more efficient than BNL2S. The NLLI estimator takes advantage of the added assumptions, and consequently its asymptotic properties depend crucially on the validity of the assumptions. Thus we are aiming at a higher efficiency at the possible sacrifice of robustness.

Assume, in addition to (8.1.1),

(8.1...

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