A generalization of the Gauss-Newton method that solves extended least-squares problems
Abstract
Modeling the mean of a random variable as a function of
unknown parameters leads to a nonlinear least-squares objective function.
The Gauss-Newton method reduces nonlinear least-squares problems to a
sequence of linear least-squares problems and requires only first-order
information about the model functions. In a more general heteroscedastic
setting, there are also unknown parameters in a model for the variance.
This leads to an objective function that is no longer a sum of squares. We
present an extension of the Gauss-Newton method that minimizes this
objective function by reducing the problem to a sequence of linear
least-squares problems.
The extension requires only first-order information.
This represents a new result because other methods that reduce this problem to a
sequence of linear least-squares problems do not necessarily converge.
