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Activity Number: 173
Type: Contributed
Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #306084
Title: A Modified Kolmogorov-Smirnov Test for Autocorrelated Data: Effective Sample Size Adjustment
Author(s): Xiaojin Xu*+ and Joseph Blitzstein
Companies: Harvard University and Harvard University
Address: Department of Statistics, Cambridge, MA, 02138, United States
Keywords: Kolmogorov-Smirnov test ; autocorrelation ; empirical process ; AR(1) process ; effective sample size

The Kolmogorov-Smirnov (K-S) test is designed to test an iid sample from a specified distribution. However, this test is not valid (does not have the claimed significance level) when there exists a sample autocorrelation. The literature of empirical process provides some theory about the asymptotic distribution of the K-S statistic when data come from an AR(1) process. Based on this, we suggest a modified K-S test with the idea of effective sample size (ESS) adjustment. It can be also easily generalized to two sample problem. Several simulation studies as well as real applications to fMRI data are provided in this paper.

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