Distribution-free minimum risk point estimation of the mean under powered absolute error loss plus cost of sampling: Illustrations with cancer data

Abstract

We begin with a discussion of results on the asymptotic properties associated with purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean when the distribution is unspecified, under squared error loss (SEL) plus the cost of sampling. We proceed to show that, given certain moment conditions, such properties can be extended to estimation problems under a broader class of loss functions, namely: first order risk-efficiency under powered absolute error loss (PAEL) plus the powered cost of sampling. In addition to purely sequential strategy, we also prove these asymptotic properties for a more operationally convenient, accelerated sequential procedure. We follow-up with extensive data analyses from simulations under mixture distributions. We conclude with illustrations using data from two cancer studies.