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Bootstrapping the empirical distribution of a linear process
Affiliation:1. Department of Mathematics & Statistics, University of Ottawa, 585 King Edward, Ottawa ON K1N 6N5, Canada;2. School of Mathematics & Statistics, University of Sydney, NSW 2006, Australia;1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany;2. Department of Computer Science and Software Engineering, Concordia University, 1455 De Maisonneuve Blvd. West, Montreal, Quebec, Canada H3G 1M8;3. Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany;1. Department of Statistics, Central China Normal University, Wuhan 430079, China;2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt;1. Department of Mathematics, University of Beira Interior, Covilhã, Portugal;2. Center of Mathematics of Minho University, Braga, Portugal;1. Department of Statistics, Amirkabir University of Technology, Tehran, Iran;2. School of Mathematics, University of Manchester, Manchester, UK
Abstract:The validity of the moving block bootstrap for the empirical distribution of a short memory causal linear process is established under simple conditions that do not involve mixing or association. Sufficient conditions can be expressed in terms of the existence of moments of the innovations and summability of the coefficients of the linear model. Applications to one and two sample tests are discussed.
Keywords:Causal linear process  Empirical process  Moving block bootstrap  Goodness of fit
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