Sequential block bootstrap in a Hilbert space with application to change point analysis
Olimjon Sh. SharipovInstitute of Mathematics, National University of Uzbekistan 29 Dormon Yoli Str., Tashkent 100125 UzbekistanJohannes TewesFakultät für Mathematik, Ruhr‐Universität Bochum 44780 Bochum GermanyMartin WendlerInstitut für Mathematik und Informatik, Ernst Moritz Arndt Universität Greifswald Germany
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Abstract A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap iterations. Thus a new functional central limit theorem for the block bootstrap in a Hilbert space is required. The test can also be used to detect changes in the marginal distribution of random vectors, which is supplemented by a simulation study. Our methods are applied to hydrological data from Germany. The Canadian Journal of Statistics 44: 300–322; 2016 © 2016 Statistical Society of Canada
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