COMPROMISE MAXIMUM-LIKELIHOOD ESTIMATORS FOR LOCATION
成果类型：
Article
署名作者：
EASTON, GS
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.2307/2290524
发表日期：
1991
页码：
1051-1064
关键词：
摘要：
This article describes a new approach for constructing robust location estimators. These estimators are constructed to be nearly optimal in small sample sizes simultaneously for two or more possible underlying shapes of the density of the data. The estimators are weighted averages of the maximum likelihood estimators for the densities considered, where the weights depend on the sample through the likelihood functions. Because of this relationship to the usual MLE's, these estimators are called compromise maximum likelihood estimators (CMLE's). For the CMLE's to exhibit good robustness properties, the densities used to construct the CMLE's should be chosen to, in a sense, span a reasonable range of possible underlying distributions of the data encountered in practice. For example, to construct CMLE's with the usual robustness properties, that is, which perform well both for narrow-tailed Gaussian data and for data containing outliers or from wide-tailed distributions, the CMLE's might be constructed based on the Gaussian distribution and a wide-tailed distribution such as the slash distribution. One would then expect that the CMLE's would perform well for data from all symmetric distributions with tails that are in between these two extremes. To verify that this is the case, Monte Carlo results are presented for CMLE's that compromise between the Gaussian and slash distributions for sample sizes 5, 10, and 20. Results are presented both for the Gaussian and slash distributions, which are used to construct the estimators, and for Student's t distributions with 2, 3, 5, 7, and 10 df, which have tails in between the Gaussian and slash extremes. The results show that the Gaussian-slash CMLE's perform better than the usual robust location estimators such as the M estimators and trimmed means. As an example of application of the estimators to real data, the behavior of the estimators for some stock portfolio return data is also examined.