2 2 2 = a--a n which shows that a2 is biased downward (i.e., it underestimates the true a2) in small samples. But notice that as n, the sample size, increases indefinitely, the second term in (15), the bias factor, tends to be zero. Therefore, asymptotically (i.e., in a very large sample), a2 is unbiased too, that is, lim E(a2) = a2 as n ^ro. It can further be proved that a2 is also a
CHAPTER FOUR: CLASSICAL NORMAL LINEAR REGRESSION MODEL (CNLRM) 117
consistent estimator4; that is, as n increases indefinitely â2 converges to its true value a2.
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