An Adaptive R-Estimate

Abstract

In 1962 Hajek proposed a test for location which was uniformly asymptotically fully efficient over a large class of distributions. Van Eeden subsequently derived the asymptotic theory for the corresponding R-estimate. Many authors have expressed reservations with regard to the small sample performance to be expected from this approach. In contrast to the methods of Hajek and Van Eeden, the procedure proposed here uses the entire data set to estimate the score function of the locally most powerful rank test. Using nearest neighbor density estimation methods, an estimate of the score function for the asymptotically most powerful grouped rank test is constructed. This function is itself a step function approximation to the score function for the locally most powerful rank test. Large sample distribution and optimality results are obtained for both the adaptive rank test and the corresponding R- estimate of location. Small sample monte-carlo results are provided.

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Document Details

Document Type
Technical Report
Publication Date
Dec 15, 1980
Accession Number
ADA096768

Entities

People

  • Michael L. Cohen

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Complex Variables
  • Contrast
  • Data Sets
  • Digital Data
  • Digital Information
  • Functions (Mathematics)
  • Mathematical Analysis
  • Mathematics
  • Mental Processes
  • Step Functions

Fields of Study

  • Mathematics

Readers

  • Statistical inference.