Estimation of the parameter of a dynamically selected population for two subclasses of the exponential family

ABSTRACT

We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non stationary scheme. We develop unbiased estimation of the parameters of the dynamically selected population and evaluate the risk of the estimators. We provide comparisons with natural estimators and obtain asymptotic results. Finally, we illustrate the applicability of the results using real data.

KEYWORDS:

• Extreme value theory
• general record models
• partial maxima
• Pfeifer model
• selected population
• uniformly minimum variance unbiased estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F12
• 62F12
• 62C07

Acknowledgments

The authors thank the anonymous referee for his/her useful comments and suggestions on an earlier version of this manuscript which resulted in this improved version.