ASYMPTOTIC EFFICIENCY OF THE KOLMOGOROV - SMIRNOV TEST

Abstract

A simple derivation of asymptotic efficiency for the Kolmogorov - Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error alpha go to zero while the type II error goes to beta, 0 < beta < 1. For symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of relative efficiencies for alternatives which approach the null hypothesis are 2/pi for normal location alternatives and 1/(pi(E)) for normal scale alternatives.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1966
Accession Number
AD0641398

Entities

People

  • Jerome Klotz

Organizations

  • University of Wisconsin Madison Department of Statistics

Tags

DTIC Thesaurus Topics

  • Air Force
  • Computations
  • Data Science
  • Distribution Functions
  • Efficiency
  • Information Science
  • Normal Distribution
  • Normality
  • Random Variables
  • Scientific Research
  • Statistics
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.