A note on bias reduction

Abstract

Let ŵ be an unbiased estimate of an unknown w ∈ R. Given a function t (w), we show how to choose a function fn (w) such that for w∗ = ŵ + fn (w), E t ( w∗ )= t (w). We illustrate this with t (w) = w a for a given constant a. For a = 2 and ŵ normal, this leads to the convolution equation cr = cr ⊗ cr . Manuscript received 10th January 2019, accepted 9th April 2020.