Nonlinear Regression on Cross-Section Data

This paper is a revised version of a paper originally en.titled Asymptotic Properties of Nonlinear Weighted Least Squares Estimators with Independem not Identically Distributed Regressors. In Section 2, the strong consistency of a class of weighted least squares (WLS) estimators is proven under general conditions, as well as the strong consistency of weighted least squares with estimated weights (EWLS). Conditions which ensure asymptotic normality of the estimators are provided in Section 3, and a general statistic for testing hypotheses is given. In Section 4, consequences of misspecification are discussed and a test for misspecification is given. Section 5 contains a summary and concluding remarks. As should be expected, the condi- tions obtained are natural extensions of those found in the fixed regressor case. Also, the unconditional covariance matrix of the parameter estimates has a more general form than the usual conditional covariance matrix