Testing for lack of fit in inverse regression—with applications to biophotonic imaging
Nicolai Bissantz,
Gerda Claeskens,
Hajo Holzmann and
Axel Munk
Journal of the Royal Statistical Society Series B, 2009, vol. 71, issue 1, 25-48
Abstract:
Summary. We propose two test statistics for use in inverse regression problems Y=Kθ+ɛ, where K is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations Y for the function θ are available. Both test statistics have a counterpart in classical hypothesis testing, where they are called the order selection test and the data‐driven Neyman smooth test. We also introduce two model selection criteria which extend the classical Akaike information criterion and Bayes information criterion to inverse regression problems. In a simulation study we show that the inverse order selection and Neyman smooth tests outperform their direct counterparts in many cases. The theory is motivated by data arising in confocal fluorescence microscopy. Here, images are observed with blurring, modelled as convolution, and stochastic error at subsequent times. The aim is then to reduce the signal‐to‐noise ratio by averaging over the distinct images. In this context it is relevant to decide whether the images are still equal, or have changed by outside influences such as moving of the object table.
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
https://doi.org/10.1111/j.1467-9868.2008.00670.x
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:71:y:2009:i:1:p:25-48
Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868
Access Statistics for this article
Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom
More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().