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Pitman closeness, monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under type II censoring. (English) Zbl 1219.62038
Summary: Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of E. H. Lloyd [Least squares estimation of location and scale parameters using order statistics. Biometrika 39, 88–95 (1952; Zbl 0046.36604)]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is that of H. N. Nagaraja [Comparison of estimators and predictors from two-parameter exponential distribution. Sankhyā, Ser. B 48, No. 1–2, 10–18 (1986; Zbl 0613.62039)], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distributions. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of the Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer than the BLIE. Next, we introduce the notions of Pitman monotonicity and Pitman consistency, and then establish that both BLUE and BLIE possess these two properties.

MSC:
62F10 Point estimation
62N01 Censored data models
62F12 Asymptotic properties of parametric estimators
65C60 Computational problems in statistics (MSC2010)
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