Optimal estimation of univariate black-box Lipschitz functions with upper and lower error bounds

Optimal estimation of univariate black-box Lipschitz functions with upper and lower error bounds

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Article ID: iaor20042275
Country: United Kingdom
Volume: 30
Issue: 10
Start Page Number: 1539
End Page Number: 1553
Publication Date: Sep 2003
Journal: Computers and Operations Research
Authors: , ,
Keywords: statistics: sampling
Abstract:

We are given an unknown univariate Lipschitz continuous function that we wish to estimate by evaluating the function sequentially at distinct points. We provide a procedure for recursively selecting this sequence of points so that, averaging over points in the domain the resulting worst case error between the estimating and actual functions is minimized. Upper and lower bounds on these errors are also provided.

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