Bias corrected sequential estimation for the mean of nef-pvf distributions

Abstract

Let F = {F_θ: θ ∈Θ} denote the class of natural exponential family of distributions having power variance function. An appropriate sequential procedure for estimating the mean μ of F_θ ∈ F under a combined loss of weighted estimation error and sampling cost is proposed. The usual estimator, namely X_t where t is an appropriate stopping time, is shown to be biased. To remedy this deficiency, we propose a class of estimators to correct for the bias. The asymptotic properties of the suggested estimators are provided. In particular, one realizes the tradeoff between the bias reduction and the reduced regret compared to the ususal estimator.