Adaptive robust estimation of location for stable distributions

Abstract

An adaptive procedure based on using two selector statistics and ,where X_p is the pth sample quantile, is described and used to choose among some robust estimators of location with respect to a class V of symmetric stable distributions with a characteristic exponent a ranging from 0.5 to 2.0 with steps of 0.1 or 0.05. The estimators considered are special symmetrical linear combinations of order statistics. Asymptotic variances of these estimators are computed using the characteristic function. Optimum asymptotic efficiencies of these estimators for the entire class V as well as for several subclasses of it are given.

Keywords:

• linear systematic statistics
• quantiles
• characteristic function
• asymptotic efficiency
• Fisherian information
• guaranteed efficiency
• selection interval
• selector statistics