Linear regression with an observation distribution model

Lichti, Derek D; Chan, Ting On; Belton, David

Linear regression with an observation distribution model

dc.contributor.author	Lichti, Derek D
dc.contributor.author	Chan, Ting On
dc.contributor.author	Belton, David
dc.date.accessioned	2021-02-08T22:03:14Z
dc.date.available	2021-02-08T22:03:14Z
dc.date.issued	2021-01-18
dc.description	This is a post-peer-review, pre-copyedit version of an article published in Journal of Geodesy. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00190-021-01484-x”	en_US
dc.description.abstract	Despite the high complexity of the real world, linear regression still plays an important role in estimating parameters to model a physical relationship between at least two variables. The precision of the estimated parameters, which can usually be considered as an indicator of the solution quality, is conventionally obtained from the inverse of the normal equations matrix for which intensive computation is required when the number of observations is large. In addition, the impacts of the distribution of the observations on parameter precision are rarely reported in the literature. In this paper, we propose a new methodology to model the distribution of observations for linear regression in order to predict the parameter precision prior to actual data collection and performing the regression. The precision analysis can be readily performed given a hypothesized data distribution. The methodology has been verified with several simulated and real datasets. The results show that the empirical and model-predicted precisions match very well, with discrepancies of up to 6% and 3.4% for simulated and real datasets, respectively. Simulations demonstrate that these differences are simply due to finite sample size. In addition, simulation also demonstrates the relative insensitivity of the method to noise in the independent regression variables that causes deviations from the data distribution function. The proposed methodology allows straightforward prediction of the parameter precision based on the distribution of the observations related to their numerical limits and geometry, which greatly simplify design procedures for various experimental setups commonly involved in geodetic surveying such as LiDAR data collection.	en_US
dc.description.grantingagency	Natural Sciences and Engineering Research Council (NSERC)	en_US
dc.identifier.citation	Lichti, D. D., Chan, T. O., & Belton, D. (2021). Linear regression with an observation distribution model. Journal of Geodesy, 95(2). doi:10.1007/s00190-021-01484-x	en_US
dc.identifier.doi	10.1007/s00190-021-01484-x	en_US
dc.identifier.grantnumber	RGPIN-2018-03775	en_US
dc.identifier.uri	http://hdl.handle.net/1880/113083
dc.identifier.uri	https://dx.doi.org/10.11575/PRISM/38638
dc.language.iso	eng	en_US
dc.publisher	Springer	en_US
dc.publisher.department	Geomatics Engineering	en_US
dc.publisher.faculty	Schulich School of Engineering	en_US
dc.publisher.hasversion	acceptedVersion	en_US
dc.publisher.institution	University of Calgary	en_US
dc.publisher.policy	https://www.springer.com/gp/open-access/publication-policies/self-archiving-policy	en_US
dc.rights	Unless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.	en_US
dc.subject	regression	en_US
dc.subject	least-squares	en_US
dc.subject	estimation	en_US
dc.subject	observation distribution	en_US
dc.subject	normal equations	en_US
dc.title	Linear regression with an observation distribution model	en_US
dc.type	journal article	en_US
ucalgary.item.requestcopy	true	en_US