Maximum Likelihood Estimation in Truncated Samples

Limit theorems for the maximum likelihood estimate under general multiply Type II censoring

“…The derivation of the asymptotic properties of the MLE is similar as that for Type II censored sample. This has been described by Halperin (1952), Bhattacharyya (1985) and others. For more general case of Multiply Type II censoring, it is yet unclear under what conditions the MLE of the parameters is consistent, asymptotically normal and asymptotically efficient.…”

“…Besides the regularity conditions for the regular Type II censoring in Halperin (1952), we have introduced (2.3)-(2.6) and the assumptions included in the theorems. Although these additional conditions seem complicated and sometime difficult to verify, they are all restrictions on the tails of the population distribution.…”

“…The estimation of 0 has been extensively studied both for complete and censored data. In the case of different censoring scheme, the maximum likelihood estimate (MLE) has been proved to be consistent, asymptotically normal and asymptotically efficient under certain regularity conditions, see Cramdr (1946), Halperin (1952), Basu and Ghosh (1980), Bhattacharyya (1985), etc.…”

On the most powerful location and scale invariant tests based on an incomplete set of order statistics

“…Note that for this test a complete sample is needed, Itowever, there are many practical situations in which only an incomplete set of order statistics (s.o.s.) is observable (see, e.g., [2,3,5,8,9]). In this paper, the critical regions of the most powerful location and scale invariant tests based on incomplete s.o.s, are presented in the case of two-parameter distributions.…”

Book Review: Statistical analysis of counting processes

“…Researchers assumed that the distribution of T was specified up to an unknown parameter 0, and F e (t) = P 0 (T < t) was usually estimated by likelihood methods. Two early important papers using this approach were those by Halperin [13] and Epstein and Sobel [8]. These parametric methods were quickly extended to situations in which data arose in comparative experiments involving two or more samples and, eventually, to some situations in which the hazard function,…”