The asymptotics of maximum likelihood and related estimators based on type II censored data. (English) Zbl 0576.62042

Bhattacharyya, Gouri K.

J. Am. Stat. Assoc. 80, 398-404 (1985).

Summary: Some simple procedures are provided for establishing the asymptotic normality and uniform strong convergence of a class of functions that arise in the context of estimating parameters from a type II censored sample. These lead to an elementary yet rigorous treatment of the asymptotic properties of maximum likelihood estimators based on type II censored data.
Further applications include the treatment of asymptotics of some modified maximum likelihood (MML) estimators. In particular, conditions are provided for the consistency and limiting normality of the MML estimators of K. G. Mehrotra and P. Nanda [Biometrika 61, 601-606 (1974; Zbl 0292.62023)], and the asymptotic efficiencies of these estimators are evaluated.

MSC:

62F12	Asymptotic properties of parametric estimators
62E20	Asymptotic distribution theory in statistics
62N05	Reliability and life testing
62G20	Asymptotic properties of nonparametric inference

Keywords:

life-test; asymptotic normality; uniform strong convergence; type II censored sample; maximum likelihood estimators; modified maximum likelihood

Citations:

Zbl 0292.62023