Minimum risk point estimation (MRPE) of the mean in an exponential distribution under powered absolute error loss (PAEL) due to estimation plus cost of sampling

Abstract

We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.

Keywords:

• Absolute error loss (AEL)
• accelerated sequential sampling
• applications
• asymptotic risk efficiency
• asymptotics
• cancer data
• first-order efficiency
• maximum likelihood estimator
• minimum risk point estimation (MRPE)
• powered AEL (PAEL)
• purely sequential sampling
• regret analysis
• sample size determination
• sampling calculus
• second-order efficiency
• simulations

SUBJECT CLASSIFICATIONS:

• 62L12
• 62L10
• 62N05

Acknowledgments

Professor John Klein gave us permission to use bone marrow data from Klein and Moeschberger (2005). We express our sincere gratitude to Professor Klein. We also thank the Associate Editor and a referee for their encouraging comments.

Disclosure

The authors have no conflicts of interest to report.