Recursively re-weighted least-squares estimation in regression models with parameterized variance

We consider a nonlinear regression model with parameterized variance and compare several methods of estimation: the Weighted Least-Squares (WLS) estimator; the two-stage LS (TSLS) estimator, where the LS estimator obtained at the first stage is plugged into the variance function used for WLS estimation at the second stage; and finally the recursively re-weighted LS (RWLS) estimator, where the LS estimator obtained after k observations is plugged into the variance function to compute the k-th weight for WLS estimation. We draw special attention to RWLS estimation which can be implemented recursively when the regression model in linear (even if the variance function is nonlinear), and is thus particularly attractive for signal processing applications.