Bias reduction by taylor series ^∗

^∗Supported in part by a Visiting Fellowship to the Australian National University.

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.

Keywords:

• bias reduction
• Taylor series
• delta method
• infinitesmal jackknife

AMS 1980 subject classification:

• Primary 62F10
• Secondary 62F12

^∗Supported in part by a Visiting Fellowship to the Australian National University.

^∗Supported in part by a Visiting Fellowship to the Australian National University.

Notes

^∗Supported in part by a Visiting Fellowship to the Australian National University.