Large sample properties of the MLE and MCLE for the natural parameter of a truncated exponential family (Q802241)

Consider a truncated exponential family of absolutely continuous distributions with natural parameter \(\theta\) and truncation parameter \(\gamma\). Strong consistency and asymptotic normality are shown to hold for the maximum likelihood and maximum conditional likelihood estimates of \(\theta\) with \(\gamma\) unknown. Moreover, these two estimates are also shown to have the same limiting distribution, coinciding with that of the maximum likelihood estimate for \(\theta\) when \(\gamma\) is assumed to be known.