ABSTRACT
As previously noted, maximum likelihood estimators are subject to certain regularity conditions that sometimes limit their usefulness. The loglikelihood function (10.3.1) is unbounded with respect to-y, and since 'Y is a lower bound on X, it follows that the value of 'Y that maximizes In L subject to this constraint is 'Y = x 1:N· Quant (1966) has shown that the MLE 'Y and & are consistent in complete samples. They are also consistent in censored samples, although bias is quite large in small samples. When 'Y is known, the asymptotic variance of & can be obtained by inverting the expected value of the second partial derivative. We accordingly differentiate (10.3.6) a second time and subsequently obtain the following approximate variance.
