Considering an estimation problem of estimating a scalar deterministic parameter $a$ from the observations $y$ which are corrupted by randomvariable $w$. The observations are $y[n] = a + w[n]$
Least Squares estimator can be used to estimate $a$ when $w$ is a White Gaussian Random Variable. This estimation method is known to be optimal. Why?
What if $w$ is from Poisson Distribtuion or some other non-gaussian, then would the estimator for $a$ be better or worse than the one found using $w$ as Gaussian r.v?