Noninformative Statistical Models: An Alternative Proof of the Cram´er–Rao Inequality under Random Censoring
We consider a model of random right censoring generated by a pair of independent random
variables and the corresponding observed sample of minima and censoring indicators. For the case
of a noninformative censoring distribution, we derive the Fisher information for the parameter of
interest and present an alternative proof of the Cram´er–Rao lower bound. The proof is based on a
direct application of the Cauchy–Bunyakovsky (Cauchy–Schwarz) inequality to the likelihood of the
censored sample, under suitable regularity conditions
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