On negative dependence properties of Latin hypercube samples and scrambled nets
Autor(en): | Doerr, Benjamin Gnewuch, Michael |
Stichwörter: | (t, m, s)-nets; Computer Science; Computer Science, Theory & Methods; Correlation number; DISCREPANCY; Latin hypercube sampling; Mathematics; Mathematics, Applied; Negative dependence; Random scrambling; SEQUENCES; Star discrepancy; VARIANCE | Erscheinungsdatum: | 2021 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal: | JOURNAL OF COMPLEXITY | Volumen: | 67 | Zusammenfassung: | We study the notion of gamma-negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to 1-negative dependence), but nevertheless it still ensures concentration of measure and allows to use large deviation bounds of Chernoff-Hoeffding-or Bernstein type. We study random variables based on random points P. These random variables appear naturally in the analysis of the discrepancy of P or, equivalently, of a suitable worst-case integration error of the quasi-Monte Carlo cubature that uses the points in P as integration nodes. We introduce the correlation number, which is the smallest possible value of gamma that ensures gamma-negative dependence. We prove that the random variables of interest based on Latin hypercube sampling or on (t, m, d)-nets do, in general, not have a correlation number of 1, i.e., they are not negative orthant dependent. (C) 2021 Elsevier Inc. All rights reserved. |
ISSN: | 0885064X | DOI: | 10.1016/j.jco.2021.101589 |
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geprüft am 14.05.2024