Spline approximation of a random process with singularity
2011 (English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758, Vol. 141, no 3, 1333-1342 p.Article in journal (Refereed) Published
Let a continuous random process X defined on [0,1] be (m+β)-smooth, 0m, 0<β1, in quadratic mean for all t>0 and have an isolated singularity point at t=0. In addition, let X be locally like a m-fold integrated β-fractional Brownian motion for all nonsingular points. We consider approximation of X by piecewise Hermite interpolation splines with n free knots (i.e., a sampling design, a mesh). The approximation performance is measured by mean errors (e.g., integrated or maximal quadratic mean errors). We construct a sequence of sampling designs with asymptotic approximation rate n^(m+β) for the whole interval.
Place, publisher, year, edition, pages
Elsevier , 2011. Vol. 141, no 3, 1333-1342 p.
Approximation, Random process, Sampling design, Hermite splines
IdentifiersURN: urn:nbn:se:umu:diva-41544DOI: 10.1016/j.jspi.2010.10.006OAI: oai:DiVA.org:umu-41544DiVA: diva2:406794