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Approximation of a Random Process by Inversion of a Kernel Density Estimator

[+] Author Affiliations
George M. Lloyd

ACTA, Torrance, CA

Paper No. IMECE2012-87974, pp. 37-44; 8 pages
doi:10.1115/IMECE2012-87974
From:
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 4: Dynamics, Control and Uncertainty, Parts A and B
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4520-2
  • Copyright © 2012 by ASME

abstract

A random process is frequently defined entirely by outcomes measured from it. Generally an important goal is to be able to approximate the random process sufficiently accurately in some sense. Common reasons for doing so are to provide surrogate variates for performing tests of hypothesis, and also to provide a model of the random process computationally suitable for inputs to or as stochastic coefficients for a numerical model. In cases of concern here the context is not limited to univariate random process, nor to Gaussian processes. This paper examines an alternative approach for modeling an arbitrary random process known only through its source variates. In this new method the kernel density estimator is inverted to provide a functional in the space of standard normal random variables. This functional can be expanded into a series representation of the random process using Wiener expansions. Several benefits accrue to this method. First, the computation expense of evaluating a KDE (and computing its inverse) need only be done once. Secondly, the rate of convergence of the series representation yields information on the departure of the random process from a strictly Gaussian one.

Copyright © 2012 by ASME

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