A Density-Quantile Function Approach to Adaptive Location or Scale Parameter Estimation

摘要

Two adaptive estimation procedures are developed for location or scale parameter estimation through the use of the asymptotically best linear unbiased estimator based on sample order statistics. The two procedures differ in their use of the data to guide optimal order statistic selection and are, consequently, termed partially and fully adaptive to indicate the associated degree of guidance. The partially adaptive procedure is developed in a data summary framework, similar to that utilized in exploratory data analysis, which provides a computationally simple scheme for obtaining estimators with high guaranteed asymptotic relative efficiency. The partially adaptive approach can also be viewed as providing techniques for adaptive data summary construction. (Author)