Minimax quadratic estimation of a quadratic functional
type: Item
instance of: scholarly article
title: Minimax quadratic estimation of a quadratic functional
zbMATH Open document ID: 0724.62039
DOI: 10.1016/0885-064X(90)90025-9
author: David Donoho
author: Michael Nussbaum
published in: Journal of Complexity
publication date: 1990-01-01T00:00:00Z
review text: Let \(f\) be a real function and consider its noisy sample observations \(v_ i=f(t_ i)+z_ i\), \(i=1,2,...,n\), where \(t_ i=-\pi +2\pi (i/n)\) are equispaced on \([-\pi,\pi]\) and the noise terms \(z_ i\) are iid \(N(0,\sigma^ 2)\). Let \(f^{(k)}(t)\) be the \(k\)th derivative of \(f\). The authors consider the estimation of the quadratic functional \(Q(f)=\int^{\pi}_{-\pi}(f^{(k)}(t))^ 2\,dt\) and derive a simple quadratic estimate which is asymptotically minimax among quadratic estimates. The given estimate is also shown to be rate optimal.
reviewed by: Rasul A. Khan
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G99
zbMATH DE Number: 4194942
zbMATH Keywords: integrated squared derivative
zbMATH Keywords: periodic function
zbMATH Keywords: incomplete data
zbMATH Keywords: noisy sample observations
zbMATH Keywords: asymptotically minimax among quadratic estimates
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4194942