To be brief, my question is what could we do when we have an estimator with a known bias.
I want to estimate the parameter $\theta$ in a distribution model.
I select an estimator $\hat\theta$ (e.g. maximum likelihood method), unfortunately according to the training data $x_i, \theta_i$, I find this estimator is biased $E(\hat\theta\mid\theta) = a \theta$, where a is a constant, e.g. $a=0.9$.
To correct this bias, I’d like to use $\hat\theta/a$ as a new unbiased estimator, does this make sense? Is there any terminology for this reduction?
And what if we have $E(\hat\theta\mid\theta) = \theta + a$, where a is constant, then make a correction $\hat\theta-a$?