Maximum likelihood estimation of the general nonlinear functional relationship with replicated observations and correlated errors

Abstract

SUMMARY The problem considered is that of estimating a p-parameter functional relationship η = η(ξ;α 1 , …, α p given replicated observations at each of n unknown values of the independent variable ξ. The errors of observation at (ξ, η) are assumed to have a bivariate normal distribution involving parameters σ 2 i , p i and r 2 i and to be independent of those at any other true point. An iterative method for obtaining maximum likelihood estimates of the structural and incidental parameters is proposed. Closed form expressions in terms of the ξ i are obtained for the asymptotic covariance matrix of estimates of the structural parameters α v and the scale incidental parameters σ v , p i and τ 2 i . An illustrative application to simulated data and a discussion of convergence are included.