This is a more general question. Suppose I have a heteroscedastic data set that I'd like to fit using IRLS (iteratively re-weighted least squares) to determine $a,b,c,d$. E.g.
$f_{model}(x) \approx a + b\, x + \epsilon(x)$,
where I assume $\epsilon(x) \sim N(0,c+d \, x)$.
We are given experimental data $f_{exp,j}(x_i)$ obtained at some set of $x_i, \; i = 1,...,n$, $j = 1,...,m$. Assume the objective function is sum of square error.
IRLS seems like a reasonable method for determining $a,b,c,d$. However, while ordinary least squares is guaranteed to have a unique solution under certain conditions, I have seen no such guarantee for IRLS, nor is one likely given the non-linear nature of the algorithm. Does anyone know under what conditions IRLS yields a unique solution? What if x is multi-variate? Perhaps it's convergent in the limit of $m \to \infty$ (large number of data points)?