In general terms my estimator is $\sum_{i=1}^n {\omega_i * x_i \over \sum _{i=1}^n {\omega_i}}$ where $x_i$ are realizations of the instrumental r.v., $w_i$ its corresponding importance weighs and $n$ is the sample size.

What is the variance of this estimator?

In general terms my estimator is $\sum_{i=1}^n {\omega_i * x_i \over \sum _{i=1}^n {\omega_i}}$ where $x_i$ are realizations of the instrumental r.v., $w_i$ its corresponding importance weighs and $n$ the sample size.

What is the variance of this estimator?