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Approximation of a Random Process with Variable Smoothness
Actuarial Department, HEC Lausanne, University of Lausanne, 1015, Lausanne, Switzerland.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia .
Department of Mathematics and Mathematical Statistics, Umeå University,Umeå, Sweden.
2015 (English)In: Mathematical Statistics and Limit Theorems: Festschrift in Honour of Paul Deheuvels / [ed] Marc Hallin, David M. Mason, Dietmar Pfeifer and Josef G. Steinebach, Springer, 2015, 189-208 p.Chapter in book (Refereed)
Abstract [en]

We consider the rate of piecewise constant approximation to a locally stationary process X(t),t ε [0,1]  , having a variable smoothness index α(t). Assuming that α(⋅)  attains its unique minimum at zero and satisfies

we propose a method for construction of observation points (composite dilated design) such that the integrated mean square error

where a piecewise constant approximation X n   is based on N(n)n  observations of X  . Further, we prove that the suggested approximation rate is optimal, and then show how to find an optimal constant K.

Place, publisher, year, edition, pages
Springer, 2015. 189-208 p.
National Category
Mathematics Mathematical Analysis Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-124315DOI: 10.1007/978-3-319-12442-1ISBN: 978-3-319-12441-4 (Print)ISBN: 978-3-319-12442-1 (online)OAI: oai:DiVA.org:liu-124315DiVA: diva2:897755
Available from: 2016-01-26 Created: 2016-01-26 Last updated: 2016-02-04

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Lifshits, Mikhail
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