Mock Exam Afternoon Query (Quant Methods)?

[samc]

Q31 of The Afternoon Mock Exam for Dec 11 candidates, makes a strange claim about estimator consistency increasing with increasing sample size. I’m not allowed to quote the question without violating CFA rules but does anyone else find the explanation of why B is correct to be unsatisfactory? Surely an estimator is either consistent or it is not, there is no measure of consistency.

 

[clearlycanadian]

As n increases, the bias in your sample decreases. Hypothetically, the bias in your sample goes to 0 as n approaches infinity. Therefore it becomes consistent as n increases because distributions of the estimators become more and more concentrated near the true value of the parameter being estimated

 

[pimpineasy]

yup as clearly canadia states

 

[samc]

But biasedness doesn’t determine consistency, an estimator can be unbiased and yet sill not consistent. In any case a sample can’t be biased; bias is a property of the estimator.
Also consistency requires convergences in probability not convergence in distribution.
Lastly it can’t ” become consistent as n increases” since consistency is always referring to the value of the estimator at the prob limit when n goes to infinity, it is a property of the estimator (or series of estimators) at the limit.
I could make my point more clearly: Increasing sample size increases the accuracy of the estimate for a consistent estimate (in some sense). What is increasing is accuracy not consistency.