Second-order (s.o.) multi-stage fixed-width confidence interval (FWCI) estimation strategies for comparing location parameters from two negative exponential (NE) populations: illustrations with cancer data

Nitis Mukhopadhyay () and Anhar Aloufi ()
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Nitis Mukhopadhyay: University of Connecticut
Anhar Aloufi: University of Connecticut

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 6, No 2, 649-680

Abstract: Abstract We consider two negative exponential (NE) populations with unknown location parameters and unknown but unequal scale parameters. We develop fixed-width confidence interval (FWCI) estimation strategies for comparing the location parameters. First, we formulate a unified multi-stage estimation strategy and derive the theory for an asymptotic second-order (s.o.) expansion of the coverage probability as well as s.o. efficiency. Next, we successively specialize by providing a range of asymptotics associated with (i) purely sequential, (ii) parallel piecewise sequential, (iii) accelerated sequential, and (iv) three-stage strategies. Theoretical findings are supplemented by simulations and real data illustrations from head and neck cancer research.

Keywords: Accelerated sequential; Data analysis; Exact consistency; First-order (f.o.) asymptotics; Negative exponential (NE); Parallel piecewise; Purely sequential; Second-order (s.o.) asymptotics; Second-order (s.o.) efficiency; Three-stage; Two-sample problem; Unequal scales; Unified theory; 62L12; 62L05; 62L10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00925-1

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