Differential and integral transformations of parametric functions in biometry

Abstract

We present some useful applications of linear statistical covariance modelling. The common classical model Y=Xβ+ε is assumed to contain at least one continuous variable in X. Treating the model as a parametric function Xβ, and applying certain linear operators on X, makes it possible to get additional information about the dependent variable Y.
In particular, it is possible to estimate derivatives, Riemann integrals and Fourier transforms of the dependent variables. The proposed methods are illustrated on real chemical data of Lake Peipsi (Estonia/Russia). Examples cover the estimation of dynamics of changes in the concentration of chemical substances in Lake Peipsi, and the estimation of the total quantity of a substance heterogeneously distributed in the lake. Calculations are carried out with the SAS software.