M-QUANTILES
成果类型：
Article
署名作者：
BRECKLING, J; CHAMBERS, R
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1988
页码：
761771
关键词：
摘要：
It is well known that a M-estimator of the centre of symmetry .theta. of a symmetric distribution can be defined in terms of either a continuous symmetric loss function .rho. or the associated influence function .psi.. This estimator is robust if .psi. is bounded. In this paper, we develop a generalization of the M-concept to estimation of a quantile analogue of .theta. called a M-quantile, by introducing a particular kind of asymmetry into .psi.. A natural consequence is that the M-quantile parameter then bears the same relationship to .theta. as the ordinary quantile bears to the median. The extension of this idea to the case of multivariate data is considered in some detail. Two applications to the analysis of agricultural survey data are given.