Compute the variance of parameter estimates given limited number of samples I'd like to infer the variance of estimated parameter $\hat\theta$ of the density function of $f(x;\theta)$ given only a limited number of samples $X_1,\cdots,X_n$.
Bootstrapping doesn't perform well when the sample size is small. Is there any other methods to deal with the case?
 A: If $f$ is tractable you may be able to compute an exact small sample variance of the estimator. Alternatively, you can use simulation from $f$ to investigate properties of the estimator. You might like to investigate the parametric bootstrap.

May I know how to compute the exact small sample variance? Compute the Fisher information??

The Fisher Information would not give the exact small sample variance. You know $f$, and you know your estimator for $\theta$, so in some cases you can compute the sampling distribution of $\hat{theta}$ under $f$.

Are there any references of computing the sampling distribution of $\hat{\theta}$ under $f$?   

For particular instances, sure, and the approaches for doing so are pretty standard (there are several different techniques that may be useful). For example (given in each case that the $X_i$ are independent), if $f$ is a gamma density and  $\hat{\theta}$ is the sample mean, then it will have a gamma density. If $f$ is uniform and $n$ is odd and $\hat{\theta}$ is a median, then it will have a beta density. This is simply a matter of being able to derive the distributions of functions of random variables; however, in practice you usually just rely on already known results, of which there are quite a few.
As mentioned, you can also simulate to any desired degree of accuracy.
