title: Element enrichment factor calculation using grain-size distribution and functional data regression.
abstract: In environmental geochemistry studies it is common practice to normalize element concentrations in order to remove the effect of grain size. Linear regression with respect to a particular grain size or conservative element is a widely used method of normalization. In this paper, the utility of functional linear regression, in which the grain-size curve is the independent variable and the concentration of pollutant the dependent variable, is analyzed and applied to detrital sediment. After implementing functional linear regression and classical linear regression models to normalize and calculate enrichment factors, we concluded that the former regression technique has some advantages over the latter. First, functional linear regression directly considers the grain-size distribution of the samples as the explanatory variable. Second, as the regression coefficients are not constant values but functions depending on the grain size, it is easier to comprehend the relationship between grain size and pollutant concentration. Third, regularization can be introduced into the model in order to establish equilibrium between reliability of the data and smoothness of the solutions.
authors.affiliation: Escuela Superior Politécnica del Litoral, Guayaquil, Ecuador.
authors.forename: C
authors.initials: C
authors.lastname: Sierra
authors.affiliation: Department of Statistics, University of Vigo, 36310 Vigo, Spain. Electronic address: ordonezcelestino@uniovi.es.
authors.forename: C
authors.initials: C
authors.lastname: Ordóñez
authors.affiliation: Campus de Mieres, Gonzalo Gutiérrez Quirós, s/n, 33600 Mieres, Asturias, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Saavedra
authors.affiliation: Department of Statistics, University of Vigo, 36310 Vigo, Spain.
authors.forename: J R
authors.initials: JR
authors.lastname: Gallego
mesh_terms: D002621:Chemistry / Q000379:methods*; D003627:Data Interpretation, Statistical; D004463:Ecology / Q000379:methods*; D004787:Environmental Pollution / Q000032:analysis*; D016014:Linear Models; D008962:Models, Theoretical; D015203:Reproducibility of Results; D012989:Soil Pollutants / Q000032:analysis*; D013030:Spain
chemical_list: D012989:Soil Pollutants
keywords: Functional regression; Normalization; Pollutant concentration; Regularization