| Abstract |
Under the squared error loss plus linear cost, we consider a problem of minimum-risk point estimation of functions of two exponential
scale parameters by a two-stage sequential procedure. We assume that 芒聙聙1 > 芒聙聙L and 芒聙聙2 > 芒聙聙G, where 芒聙聙L, 芒聙聙G > 0 are known
to the experimenter from past experiences and look into the estimation of functions of two exponential scale parameters, 芒聙聙 = h(芒聙聙1, 芒聙聙2),
where h(芒聙聙1, 芒聙聙2) is a positive real-valued, three-times continuously differential function defined in R2+. The proposed two-stage procedure is shown to enjoy all the usual first-order properties. As a follow-up, we include a simulation
study on two specific parameters of the form (芒聙聙1/芒聙聙2)r, r > 0 and |芒聙聙1 芒聢聮 芒聙聙2|.
Simulation results show that on the average, the stopping rule N of the proposed procedure is a good estimate of the optimal sample
size n芒聙聙, that is, E[N/n芒聙聙] a.s. 芒聢聮! 1. Furthermore as c ! 0, the ratio of the risk associated with N and the risk associated with n芒聙聙 converges to 1, that is,
lim c!0RN(c)/Rn芒聙聙 (c) = 1 suggesting that the two-stage procedure is asymptotically risk efficient. |
Mindanao State
University - Iligan Institute of Technology