Seminar at SMU Delhi

We discuss Stein-type two-stage, modified two-stage and purely sequential strategies to estimate an unknown negative exponential location with an unknown scale parameter under a newly defined and modified Linex loss function. We introduce a notion of risk per cost function which is shown to be bounded above by a constant. Both asymptotic first- and second-order properties for the modified two-stage and purely sequential estimation strategies will be elaborated. The results will be supported by an extensive set of data analysis carried out via computer simulations for a wide variety of sample sizes. We observe that both modified two-stage and purely sequential estimation strategies perform remarkably well unlike the Stein-type two stage methodology. We also illustrate the implementation of the latter methodologies using a real dataset from health studies, namely, infant mortality data. An extension to a two sample problem is also discussed briefly.