Linear Estimators and Predictors Based on Generalized Order Statistics from Generalized Pareto Distributions

Abstract

Linear estimation and prediction based on several samples of generalized order statistics from generalized Pareto distributions is considered. Representations of best linear unbiased estimators (BLUEs) and best linear equivariant estimators in location-scale families are derived, as well as corresponding optimal linear predictors. Moreover, we study positivity of the linear estimators of the scale parameter. An example illustrates that the BLUE may attain negative values with positive probability in certain situations.

Keywords:

• BLUE
• best linear unbiased estimator
• BLEE
• Best linear invariant estimator
• BLIE
• Non-Negativity of BLUE
• Best linear unbiased predictor
• BLUP
• Best linear invariant predictor
• Exponential distribution
• Location and scale parameters
• Pareto distribution
• Uniform distribution

Mathematics Subject Classification:

• Primary 62N02
• Secondary 62G30, 62N05, 62F10

Acknowledgment

The author thanks an anonymous referee for helpful comments leading to an improved version of the article.