The Dagum and auxiliary covariance families: Towards reconciling two-parameter models that separate fractal dimension and the Hurst effect

Maria Dolores Ruiz-Medina, Emilio Porcu, Rosaura Fernandez-Pascual

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The functional statistical framework is considered to address the problem of least-squares estimation of the realizations of fractal and long-range dependence Gaussian random signals, from the observation of the corresponding response surface. The statistical methodology applied is based on the functional regression model. The geometrical properties of the separable Hilbert spaces of functions, where the response surface and the signal of interest lie, are considered for removing the ill-posed nature of the estimation problem, due to the non-locality of the integro-pseudodifferential operators involved. Specifically, the local and asymptotic properties of the spectra of fractal and long-range dependence random fields in the Linnik-type, Dagum-type and auxiliary families are analyzed to derive a stable solution to the associated functional estimation problem. Their pseudodifferential representation and Reproducing Kernel Hilbert Space (RKHS) characterization are also derived for describing the geometrical properties of the spaces where the functional random variables involved in the corresponding regression problem can be found.

Original languageBritish English
Pages (from-to)259-268
Number of pages10
JournalProbabilistic Engineering Mechanics
Volume26
Issue number2
DOIs
StatePublished - Apr 2011

Keywords

  • Dagum family
  • Functional regression
  • Hausdorff dimension
  • Hurst index
  • Mean-square Hlder exponent
  • Response surface
  • RKHS
  • Sobolev spaces
  • Statistical Volume Element
  • Thermoelasticity

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