I'm wondering if there is a difference between an asymptotically unbiased estimator and a consistent estimator.
For asymptotically unbiased estimators, the expected value of the estimator converges to the parameter, while for a consistent estimator, the estimator converges in probability to the parameter.
These sound nearly identical, but I believe that being consistent might actually be stronger than being asymptotically unbiased, since being consistent, i.e. converging in probability, implies that not only will the estimates be roughly centered around the true value, but will also be getting closer to it as n increases.
Can someone confirm or refute this claim?
