eprintid: 1868
rev_number: 8
eprint_status: archive
userid: 2
dir: disk0/00/00/18/68
datestamp: 2017-02-08 07:45:34
lastmod: 2018-03-28 12:05:03
status_changed: 2017-02-08 07:45:34
type: article
metadata_visibility: show
creators_name: Anderson, Theodore Wilbur
creators_name: Darling, Donald Allan
corp_creators: Columbia University, USA
corp_creators: University of Michigan, USA
title: Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
subjects: MP2_2
divisions: EPOS-IP
full_text_status: none
keywords: Weighting functions, Stochastic processes, Mathematical functions, Distribution functions, Differential equations, Eigenvalues, Eigenfunctions, Statistics, Mathematical integrals
abstract: The statistical problem treated is that of testing the hypothesis that n independent, identically distributed random variables have a specified continuous distribution function F(x). If Fn(x) is the empirical cumulative distribution function and ψ(t) is some nonnegative weight function (0 ≤ t ≤ 1), we consider n^1/2 sup (-∞<x<∞) {|F(x)-Fn(x)|ψ^1/2[F(x)]} and n∫[F(x)-Fn(x)]^2ψ[F(x)]dF(x). a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations. For certain weight functions including ψ=1 and ψ=1/[t(1-t)] we give explicit limiting distributions. A table of the asymptotic distribution of the von Mises ω^2 criterion is given.
date: 1952-06
date_type: published
publication: The Annals of Mathematical Statistics
volume: 23
number: 2
publisher: The Institute of Mathematical Statistics
pagerange: 193-212
issn: 0003-4851
official_url: http://www.jstor.org/stable/2236446
access_IS-EPOS: limited
software_references: Inter-event_Time_Distribution_Analysis
owner: Publisher
citation:   Anderson, Theodore Wilbur and Darling, Donald Allan  (1952) Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes.  The Annals of Mathematical Statistics, 23 (2).  pp. 193-212.