DISCREPANCY BOUNDS FOR A CLASS OF NEGATIVELY DEPENDENT RANDOM POINTS INCLUDING LATIN HYPERCUBE SAMPLES
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Gnewuch, Michael | |
dc.contributor.author | Hebbinghaus, Nils | |
dc.date.accessioned | 2021-12-23T16:11:10Z | - |
dc.date.available | 2021-12-23T16:11:10Z | - |
dc.date.issued | 2021 | |
dc.identifier.issn | 10505164 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/9565 | - |
dc.description.abstract | We introduce a class of gamma-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a gamma-negatively dependent N-point sample in dimension d we provide probabilistic upper bounds for its star discrepancy with explicitly stated dependence on N, d, and gamma. These bounds generalize the probabilistic bounds for Monte Carlo samples from Heinrich et al. (Acta Arith. 96 (2001) 279-302) and C. Aistleitner (J. Complexity 27 (2011) 531-540), and they are optimal for Monte Carlo and Latin hypercube samples. In the special case of Monte Carlo samples the constants that appear in our bounds improve substantially on the constants presented in the latter paper and in C. Aistleitner and M. T. Hofer (Math. Comp. 83 (2014) 1373-1381). | |
dc.description.sponsorship | Australian Research Council ARCAustralian Research Council; Part of the work of Michael Gnewuch was done while he was a research fellow and a visitor at the School of Mathematics and Statistics of the University of New South Wales in Sydney and a ``Chercheur Invite'' at the Laboratoire d'Informatique (LIX) of Ecole Polytechnique in Paris, France. He acknowledges support from the Australian Research Council ARC and thanks his hosts Josef Dick, Frances Y. Kuo, Ian H. Sloan, and Benjamin Doerr for their hospitality. | |
dc.language.iso | en | |
dc.publisher | INST MATHEMATICAL STATISTICS-IMS | |
dc.relation.ispartof | ANNALS OF APPLIED PROBABILITY | |
dc.subject | CONSTRUCTION | |
dc.subject | ERROR-BOUNDS | |
dc.subject | INTEGRATION | |
dc.subject | Latin hypercube sampling | |
dc.subject | Mathematics | |
dc.subject | MONTE-CARLO VARIANCE | |
dc.subject | Negatively dependent random variables | |
dc.subject | NUMBERS | |
dc.subject | padding by Monte Carlo | |
dc.subject | pre-asymptotic bounds | |
dc.subject | quasi-Monte Carlo Sampling | |
dc.subject | star discrepancy | |
dc.subject | STAR-DISCREPANCY | |
dc.subject | Statistics & Probability | |
dc.subject | TRACTABILITY | |
dc.subject | VARIABLES | |
dc.title | DISCREPANCY BOUNDS FOR A CLASS OF NEGATIVELY DEPENDENT RANDOM POINTS INCLUDING LATIN HYPERCUBE SAMPLES | |
dc.type | journal article | |
dc.identifier.doi | 10.1214/20-AAP1638 | |
dc.identifier.isi | ISI:000696242300014 | |
dc.description.volume | 31 | |
dc.description.issue | 4 | |
dc.description.startpage | 1944 | |
dc.description.endpage | 1965 | |
dc.publisher.place | 3163 SOMERSET DR, CLEVELAND, OH 44122 USA | |
dcterms.isPartOf.abbreviation | Ann. Appl. Probab. | |
dcterms.oaStatus | Green Submitted | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | GnMi297 | - |
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