Estimation for the nonlinear functional relationship

Estimation of the parameters of the nonlinear functional model with known error covariance matrix is discussed. Asymptotic properties of the maximum likelihood estimator for the implicit functional model are presented. The approximate bias in the maximum likelihood estimator due to the nonlinearity of the relationship is given and a bias-adjusted estimator is suggested. Numerical and theoretical results support the superiority of the bias-adjusted estimator relative to the maximum likelihood estimator.