On Ecological Aspects of Dynamics for Zero Slope Regression for Water Pollution in Chile

0504430 - ÚI 2020 RIV US eng J - Journal Article
Stehlík, M. - Núñez Soza, L. - Fabián, Zdeněk - Jiřina, Marcel - Jordanova, P. - Arancibia, S. C. - Kiselák, J.
On Ecological Aspects of Dynamics for Zero Slope Regression for Water Pollution in Chile.
Stochastic Analysis and Applications. Roč. 37, č. 4 (2019), s. 574-601. ISSN 0736-2994. E-ISSN 1532-9356
R&D Projects: GA MŠMT(CZ) EF16_013/0001787
Institutional support: RVO:67985807
Keywords : robust regression * score regression * non-normal distribution of residuals * boron * arsenic
OECD category: Statistics and probability
Impact factor: 1.035, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1080/07362994.2019.1592692

Zero slope regression is an important problem in chemometrics, ranging from challenges of intercept-bias and slope ‘corrections’ in spectrometry, up to analysis of administrative data on chemical pollution in water in the region of Arica and Parinacota. Such issue is really complex and it integrates problems of optimal design, symmetry of errors, stabilization of the variability of estimators, dynamical system for errors up to an administrative data challenges. In this article we introduce a realistic approach to zero slope regression problem from dynamical point of view. Linear regression is a widely used approach for data fitting under assumption of normally distributed residuals. Many times non-normal residuals are observed and also theoretically justified. Our solution to such problem uses the recently introduced inference function called score function of distribution. As a minimization criterion, the minimum information of residuals criterion is used. The score regression appears to be a direct generalization of the least-squares regression for an arbitrary known (believed) distribution of residuals. The score estimation is also distribution sensitive version of M-estimation. The capability of the method is demonstrated by water pollution data examples.
Permanent Link: http://hdl.handle.net/11104/0296064