Approximation of a Random Process with Variable Smoothness
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)
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.
Mathematics Mathematical Analysis Computational Mathematics
IdentifiersURN: 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