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Approximation of a Random Process with Variable Smoothness
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: Mathematical Statistics and Limit Theorems: Festschrift in Honour of Paul Deheuvels / [ed] Hallin, Marc; Mason, David M.; Pfeifer, Dietmar; Steinebach, Josef G., Springer International Publishing , 2015, 189-208 p.Chapter in book (Other academic)
Abstract [en]

We consider the rate of piecewise constant approximation to a locally stationary process X(t),t∈[0,1] , having a variable smoothness index α(t) . Assuming that α(⋅) attains its unique minimum at zero and satisfies α(t)=α0+btγ+o(tγ) as t→0, we propose a method for construction of observation points (composite dilated design) such that the integrated mean square error ∫10E{(X(t)−Xn(t))2}dt∼Knα0(logn)(α0+1)/γ as n→∞, where a piecewise constant approximation Xn 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 International Publishing , 2015. 189-208 p.
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-103713DOI: 10.1007/978-3-319-12442-1_11ISBN: 978-3-319-12441-4OAI: diva2:814901

Originally published in manuscript form.

Available from: 2015-05-28 Created: 2015-05-28 Last updated: 2015-05-28Bibliographically approved

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Seleznjev, Oleg
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