Asymptotically-unbiased estimator

A concept indicating that the estimator is unbiased in the limit (cf. Unbiased estimator). Let be a sequence of random variables on a probability space , where is one of the probability measures in a family . Let a function be given on the family , and let there be a sequence of -measurable functions , the mathematical expectations of which, , are given. Then, if, as ,

one says that is a function which is asymptotically unbiased for the function . If one calls "observations" and "estimators" , one obtains the definition of an asymptotically-unbiased estimator. In the simplest case of unlimited repeated sampling from a population, the distribution of which depends on a one-dimensional parameter , an asymptotically-unbiased estimator for , constructed with respect to the sample size , satisfies the condition

for any , as .