An extension of the Gauss–Newton algorithm for estimation under asymmetric loss

Estimators obtained by the use of the relevant loss function lead to forecasts with good properties when the same loss function is used to evaluate the forecasts. The provided extension of the Gauss–Newton algorithm is tailored for the associated optimization problem. Due to an approximation of the second derivative of the loss function, it can be viewed as a succession of linear generalized least-squares regressions and is easy to implement. Smoothing loss functions which do not possess derivatives has asymptotic validity. The extension performs well compared to the Newton (with exact Hessian) and BFGS algorithms in a Monte Carlo study employing different loss functions and several autoregressive models.