Definition of Asymptotically Unbiased

Definition: "There are at least three possible definitions of asymptotic unbiasedness:

1. The mean of the limiting distribution of n^.5(t_hat - t) is zero.

2. lim_n->infinity E[t_hat] = t.

3. plim t_hat = t."

Usually an estimator will have all three of these or none of them. Cases exist however in which left hand sides of those three are different. "There is no general agreement among authors as to the precise meaning of asymptotic unbiasedness, perhaps because the term is misleading at the outset; asymptotic refers to an approximation, while unbiasedness is an exact result. Nonetheless the majority view seems to be that (2) is the proper definition of asymptotic unbiasedness. Note, though, that this definition relies upon quantities that are generally unknown and that may not exist." -- Greene, p 107 (Econterms)

Terms related to Asymptotically Unbiased:

• Asymptotic
• Asymptotic variance
• Asymptotic normality
• Asymptotically Equivalent

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Writing a Term Paper? Here are a few starting points for research on Asymptotically Unbiased:

Books on Asymptotically Unbiased:

• Greene, William H.. 1997. Econometric Analysis. 3nd edition.
  Macmillan Publishing Company.

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