Use of Weighted Least-Squares Splines for Calibration in Analytical Chemistry

Abstract

Weighted least-squares spline functions are discussed and applied for calibration processes in analytical chemistry. Different weighting techniques are also considered, and for the evaluation of the results some quality coefficients are proposed. Depending upon the structure of the data, some weighting procedures may improve the results dramatically. Considering the results obtained in the case of TLC densitometry, it seems that nonlinear weighting procedures based upon the distance to the function are the best ones, with a plus for the y-distance type. It is difficult to give general rules regarding the optimal parameters of the weighted calibration splines-function order (m), number (N) and distribution of knots, and weighting technique. These depend upon the structure of the data. However, higher order splines are not recommended since the result might become extremely unstable. The example used to illustrate the performances of the procedures discussed here involved only a single independent variable. The method is general and extends practically to any number of variables, thus resulting in a multivariate approach.

Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

“…This constitutes heteroscedastic data. A weighted regression is used to address this problem [17,19,42,43]. The value of the weight must be determined for a weighted regression.…”