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. Issue 2 (2nd April 2020)

• Record Type: Journal Article
• Authors: Mukhopadhyay, Nitis; Khariton, Yakov
• Is Part Of: Sequential analysis. Volume 39:Issue 2(2020)
• Page Start: 241
• Page End: 268
• Publication Date: 2020-04-02
• Subjects: 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; 62L12 -- 62L10 -- 62N05; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2020.1766930
• Languages: English
• ISSNs: 0747-4946

Abstract

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.