Zhou X H
Department of Medicine, Indiana University School of Medicine, Indianapolis 46202-5119, USA.
Stat Med. 1998 Oct 15;17(19):2251-64. doi: 10.1002/(sici)1097-0258(19981015)17:19<2251::aid-sim925>3.0.co;2-w.
The most commonly used estimator for a log-normal mean is the sample mean. In this paper, we show that this estimator can have a large mean square error, even for large samples. Then, we study three main alternative estimators: (i) a uniformly minimum variance unbiased (UMVU) estimator; (ii) a maximum likelihood (ML) estimator; (iii) a conditionally minimal mean square error (MSE) estimator. We find that the conditionally minimal MSE estimator has the smallest mean square error among the four estimators considered here, regardless of the sample size and the skewness of the log-normal population. However, for large samples (n > or = 200), the UMVU estimator, the ML estimator, and the conditionally minimal MSE estimators have very similar mean square errors. Since the ML estimator is the easiest to compute among these three estimators, for large samples we recommend the use of the ML estimator. For small to moderate samples, we recommend the use of the conditionally minimal MSE estimator.
对数正态均值最常用的估计量是样本均值。在本文中，我们表明即使对于大样本，该估计量也可能具有较大的均方误差。然后，我们研究了三种主要的替代估计量：（i）一致最小方差无偏（UMVU）估计量；（ii）最大似然（ML）估计量；（iii）条件最小均方误差（MSE）估计量。我们发现，在所考虑的这四个估计量中，条件最小MSE估计量具有最小的均方误差，与样本大小和对数正态总体的偏度无关。然而，对于大样本（n≥200），UMVU估计量、ML估计量和条件最小MSE估计量具有非常相似的均方误差。由于ML估计量在这三个估计量中最容易计算，对于大样本，我们建议使用ML估计量。对于小到中等样本，我们建议使用条件最小MSE估计量。
