Optimal designs for indirect regression

Biedermann, Stefanie, Bissantz, Nicolai, Dette, Holger and Jones, Edmund (2011) Optimal designs for indirect regression. Inverse Problems, 27, (10), 105003. (doi:10.1088/0266-5611/27/10/105003).


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In many real life applications, it is impossible to observe the feature of interest directly. For example, scientists in Materials Science may be interested in detecting cracks inside objects, not visible from the outside. Similarly, non-invasive medical imaging techniques such as Positrone Emission Tomography rely on indirect observations to reconstruct an image of the patient's internal organs. In this paper, we investigate optimal designs for such indirect regression problems. We determine designs minimizing the integrated mean squared error of estimates of the regression function obtained by Tikhonov or spectral
cut-off regularization. We use the optimal designs as benchmarks to investigate the efficiency of the uniform design commonly used in applications. Several examples are discussed to illustrate the results, in most of which the uniform design or a simple modification thereof is demonstrated to be very efficient for the estimation of the regression function. Our designs provide guidelines to
scientists regarding the experimental conditions at which the indirect observations should be taken in order to obtain an accurate estimate for the object of

Item Type: Article
Digital Object Identifier (DOI): doi:10.1088/0266-5611/27/10/105003
ISSNs: 0266-5611 (print)
1361-6420 (electronic)
Related URLs:
Keywords: indirect regression, optimal design, uniform design, integrated mean squared error criterion, Tikhonov regularization, spectral cut-off, regularization, radon transform
Subjects: H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
Faculty of Social and Human Sciences > Mathematical Sciences > Statistics
ePrint ID: 163499
Accepted Date and Publication Date:
16 September 2011Published
Date Deposited: 09 Sep 2010 09:08
Last Modified: 31 Mar 2016 13:29
URI: http://eprints.soton.ac.uk/id/eprint/163499

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