Sorry for my broken English at first.

Consider two samples $X_{1}, \cdots ,X_{m}$ and $Y_{1}, \cdots ,Y_{n}$ where $X_{i} \thicksim N(\mu_{1}, \sigma_{1}^2), i.i.d.$ and $Y_{j} \thicksim N(\mu_{2}, \sigma_{2}^2), i.i.d.$.

Say that both $\mu_{1}$ and $\mu_{2}$ are unknown. Then, what will be an unbiased estimator of the ratio of variances? I mean, unbiased estimator of this; 
$$\frac{\sigma_{2}^2}{\sigma_{1}^2}$$
And how to proof that?

All of statistics textbooks that I have don't explain the things above. 
I would appreciate if you help me.