 On the empirical process of strongly dependent stable random variables: asymptotic properties, simulation and applicationsEmanuele Taufer Statistics & Probability Letters, 2015, vol. 106, issue C, 262-271 Abstract: This paper analyzes the limit properties of the empirical process of α-stable random variables with long range dependence. The α-stable random variables are constructed by non-linear transformations of bivariate sequences of strongly dependent gaussian processes. The approach followed allows an analysis of the empirical process by means of expansions in terms of bivariate Hermite polynomials for the full range 0<α<2. A weak uniform reduction principle is provided and it is shown that the limiting process is gaussian. The results of the paper differ substantially from those available for empirical processes obtained by stable moving averages with long memory. An application to goodness-of-fit testing is discussed. Keywords: Empirical process; Stable distribution; Hermite polynomial; Goodness-of-fit; Kolmogorov–Smirnov; Long range dependence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:106:y:2015:i:c:p:262-271 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2015.07.032 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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