Sequential Estimation of the Shape Parameter of the Pareto Distribution

摘要

The problem addressed is that of sequentially estimating θ, the shape parameter of the type I Pareto distribution, subject to the loss function where c is a known cost per observation and is the maximum likelihood estimator of θ. We propose a stopping time t and provide a second-order asymptotic expansion, as c → 0 , for the regret incurred by the sequential procedure under the loss L _(c ). We also show that the point estimator is asymptotically unbiased for θ.