A New Perspective in Functional EIV Linear Models: Part II

Ali Al-Sharadqah and Nicholas Woolsey

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 4, 856-873

Abstract: In Error-in-Variables (EIV) models, all variables are subject to error and their estimators are heavily biased especially in the case of small sample sizes. This paper extends the results of Al-Sharadqah and proposes a new estimator for the problem of fitting 3D planes to data. Instead of minimizing an objective function obtained by the likelihood principles or others, a family of objective functions depending on an unknown smooth weight is considered. Then, the optimal weight function is derived so that the minimizer of the corresponding objective function has a zero second-order bias. To derive such a weight, a general form of the second-order bias is derived by applying our perturbation theory. This leads to a system of two first-order linear partial differential equations that admits a unique solution. The explicit formula of the weight is derived yielding the objective function. This turns to be a standard nonlinear least squares problem. Accordingly, the Levenberg-Marquardt (LM) algorithm is implemented. Finally, the effectiveness and superiority of our method are assessed by a series of numerical experiments.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2019.1642493 (text/html)
Access to full text is restricted to subscribers.

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:taf:lstaxx:v:50:y:2021:i:4:p:856-873

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2019.1642493

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().