Bias reduction by Taylor series
Bias reduction by Taylor series
复制标题
通过泰勒级数减少偏差
DOI：
10.1080/03610928708829512
复制
发表时间：
1987
影响因子：
0.8
通讯作者：
C. Withers
中科院分区：
文献类型：
--
作者：
C. Withers
我们考虑估计一个函数（比如\(t(\theta)\)）的问题，已知一个估计量，其分布由未知向量\(\theta\)确定。通常该估计量具有\(O(n^{n - 1})\)的偏差，记为\(\sim n^{-1}\)，并且需要\(\sim n\)次计算，其中\(n\)是样本量（对于多个样本来说是最小样本量）。对于一大类估计量以及任何给定的\(k\)，我们展示了如何构造一个\(t(\theta)\)的估计量，其偏差为\(\sim n^{-k}\)，但仍然只需要\(\sim n\)次计算。对于\(k \leq 4\)，给出了一个明确的公式。当无偏估计量作为\(n\)的函数形式已知时，该方法可以扩展以给出无偏估计量。
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.