Recursively re-weighted Least-Squares estimation in regression models with parameterized variance
Luc Pronzato and Andrej Pazman
(2004) Technical Report. Luc Pronzato, Sophia Antipolis.

## Abstract

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 {\em recursively} when the regression model in linear (even if the variance function is nonlinear), and is thus {\em particularly attractive for signal processing applications}