Bias reduction by taylor series∗

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Abstract
We consider the problem of estimating a function say t(θ) , given an estimate with distribution determined by the unknown vector θ. Typically has bias 0O(nn –1), written ∼ n –1, and requires ∼ n calculations, where n is the sample size (or minimum sample size for more than one sample). For a wide class of estimates and any given k,we show how to construct an estimate of t(θ) with bias ∼ n –kwhich still requires only ∼ n calculations. For k ≤4 an explicit formula is given. The method can be extended to give unbiased estimates (UEs) when their form as a function of n is known.

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