CONSISTENCY OF ESTIMATES

An estimator is asymptotically unbiased if the bias approaches zero with the number of data tending to infinity. It is reasonable that as the number of data increases the estimate tends to the true value; this is a property called ‘‘consistency.’’ It is a stronger property than asymptotic unbiasedness because it has to be satisfied for every single realization of estimates. All the consistent estimates are unbiased asymptotically. This convergence is required to be with probability 1 (one):

lim P{|b(zi, Z2,…, zn) — b < 5} = 1; 8 5 > 0

Nn

The probability that the error in estimates (with respect to the true values) is less than a certain small positive value is one.