Optimal global rates of convergence for interpolation problems with random design

Michael Kohler and Adam Krzyżak

Statistics & Probability Letters, 2013, vol. 83, issue 8, 1871-1879

Abstract: Given a sample of a d-dimensional design variable X and observations of the corresponding values of a measurable function m:Rd→R without additional errors, we are interested in estimating m on whole Rd such that the L1 error (with integration with respect to the design measure) of the estimate is small. Under the assumption that the support of X is bounded and that m is (p,C)-smooth (i.e., roughly speaking, m is p-times continuously differentiable) we derive the minimax lower and upper bounds on the L1 error.

Keywords: Interpolation; L1-error; Minimax rate of convergence; Random design (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1016/j.spl.2013.04.018

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