Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis. Issue 3 (2nd July 2016) - Mukhopadhyay, Nitis; Bapat, Sudeep R.
ABSTRACT: We have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016, Sequential Analysis ). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984, Canadian Journal of Statistics ) and Mukhopadhyay and Darmanto (1988, Sequential Analysis ). We have resorted to Mukhopadhyay and Duggan (1997, Sankhya, Series A ) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977, 1979, Annals of Statistics ) and Woodroofe (1977, Annals of Statistics ) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both modified two-stage and purely sequential methods perform very well. Both methodologies are also illustrated and implemented using real datasets from cancer studies and reliability analysis.