Assessing the number of mean square derivatives of a Gaussian process

Delphine Blanke and Céline Vial

Stochastic Processes and their Applications, 2008, vol. 118, issue 10, 1852-1869

Abstract: We consider a real Gaussian process X with unknown smoothness where the mean square derivative X(r0) is supposed to be Hölder continuous in quadratic mean. First, from selected sampled observations, we study the reconstruction of X(t), t[set membership, variant][0,1], with a piecewise polynomial interpolation of degree r>=1. We show that the mean square error of the interpolation is a decreasing function of r but becomes stable as soon as r>=r0. Next, from an interpolation-based empirical criterion and n sampled observations of X, we derive an estimator of r0 and prove its strong consistency by giving an exponential inequality for . Finally, we establish the strong consistency of with an almost optimal rate.

Keywords: Inference; for; Gaussian; processes; Holder; regularity; Piecewise; Lagrange; interpolation; Regular; sequences (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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