# Reference request: parameter inference on simulated distribution

Say I have some data $(x_{1},\ldots,x_{n})$ which I believe to be drawn from some distribution $\nu_{\theta}(x)$. I'm moderately familiar with estimation techniques for $\theta$ when I have some functional form for $\nu_{\theta}(x)$.

However I'm wondering if someone can give me an introductory reference (or at least the best words to google) for when all I can do is simulate from $\nu_{\theta}(x)$ and so want to do inference with respect to the estimated distribution $\hat \nu_{\theta}(x)$.

My naive approach would be to construct an empirical cdf from my data $\hat{F}(x)$ and then use the KS metric to determine the closest distribution. More specifically, I let \begin{equation} \hat\theta=\text{argmin}_{\theta}\sup_{x}|\hat\nu_{\theta}(x)-\hat{F}(x)| \end{equation} but then what are the statistical properties of this estimator?

When $\nu_\theta$ is the true cdf, this method is called minimum distance estimation and there are consistency results in the literature. Since you can approximate $\nu_\theta$ with an arbitrary precision by simulating enough points, the above results extend to this case.