Let's say we estimate a parameter, $\theta$, by $\hat{\theta}$. For this estimator we have the following property that $$\hat{\theta}\to_{p}\theta+f(\theta)$$
where $\to_{p}$ denotes convergence in probability and $f(\theta)$ is a random function indexed by $\theta$. I am now wondering if there is a way to reduce the bias? Let's say, I calculate the expected value of $f(\theta)$ but then it is indexed by $\theta$ hence I cannot subtract this mean from $\hat{\theta}$ to reduce the bias. Is there any way to tackle this problem?
Many thanks for your help.