Goodness-of-Fit Based on Integrated Squared Discrepancies Between Sample and Population Characteristic Functions,

Abstract

This document assesses the feasibility of a goodness-of-fit test based on an integral of the weighted squared modulus of the discrepancy between the sample and population characteristic functions. The resulting statistic is therefore analogous to the Cramer-von Mises statistic and is shown to reduce to it as a special case. A number of properties of the test have been derived, including the asymptotic null distribution of its statistic. It is shown that under mild regularity conditions the test is consistent. A number of approximations to the null distribution of the test statistic are considered, and are found to be successful in simplifying its application without due loss of accuracy. Keywords: Sample characteristic function; Goodness-of-fit; Weighted sum of chi-squared variates; Consistency; Asymptotic distribution; Rate of convergence; Cumulants. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA178763

Entities

People

  • A. S. Paulson
  • J. L. Bryant

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Covariance
  • Data Science
  • Distribution Functions
  • Eigenvalues
  • Equations
  • Goodness Of Fit Tests
  • Hilbert Space
  • Information Science
  • Integral Equations
  • New York
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Inference
  • Statistics
  • Theorems
  • Weighting Functions

Fields of Study

  • Mathematics

Readers

  • Statistical inference.