THE SIGN TEST ON AUTOREGRESSIVE DATA.

Abstract

The sign test is analyzed and shown to lose its distribution-free properties for dependent data of the form Xsubt = pXsubt-1 + Wsubt, t = 1, ..., N, O p < 1; (Wsubt) is a strictly stationary sequence of independent, identically distributed random variables with zero mean. Formulas for the mean and variance of the sign test statistic are derived and examples given for Xsubt being Gaussian and double-exponential. The Blum-Rosenblatt Central Limit Theorem for strong mixing processes is used to prove asymptotic normality of the sign test statistic in these two cases. Anomalous results of a Monte Carlo experiment are reported. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1965
Accession Number
AD0625272

Entities

People

  • H. Rubin
  • J. Gastwirth
  • S. S. Wolff

Organizations

  • Johns Hopkins University

Tags

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Computing-Related Activities
  • Cooperation
  • Data Science
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Mathematics
  • Michigan
  • Normality
  • Random Variables
  • Sequences
  • Stationary
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Distributed Systems and Data Platform Development
  • Statistical inference.