SEQUENTIAL ESTIMATION IN A SUBCLASS OF EXPONENTIAL FAMILY UNDER WEIGHTED SQUARED ERROR LOSS

Abstract

In a subclass of the scale-parameter exponential family, we consider the sequential pointestimation of a function of the scale parameter under the loss function given as the sum of the weightedsquared error loss and a linear cost. For a fully sequential sampling scheme, second order expansions areobtained for the expected sample size as well as for the regret of the procedure. The former researches onGamma and Exponential distributions can be deduced from our general results.