Pitman closeness, monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under Type II censoring

• Published in: Journal of statistical computation and simulation Vol. 81; no. 8; pp. 985 - 999
• Main Authors: Balakrishnan, N., Davies, Katherine F., Keating, Jerome P., Mason, Robert L.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.08.2011; Taylor & Francis Ltd
• Subjects: best linear invariant estimator; best linear unbiased estimator; Comparative analysis; Consistency; Criteria; Estimating techniques; Estimators; Grounds; Invariants; Least squares method; order statistics; Parameter estimation; Pitman closeness; Pitman consistency; Pitman monotonicity; probabilities of closeness; Probability distribution; Samples; Statistics; Type II censoring
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949651003587684

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 Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88-95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhyā Ser. B 48 (1986), pp. 10-18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. 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 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.