Use of weighted least-squares splines for calibration in analytical chemistry

Weighted least-squares spline functions are discussed and applied for calib ration processes in analytical chemistry. Different weighting techniques ar e also considered, and for the evaluation of the results some quality coeff icients are proposed. Depending upon the structure of the data, some weight ing procedures may improve the results dramatically. Considering the result s obtained in the case of TLC densitometry, it seems that nonlinear weighti ng procedures based upon the distance to the function are the best ones, wi th a plus for the gamma-distance type. It is difficult to give general rule s regarding the optimal parameters of the weighted calibration splines-func tion order (m), number (N) and distribution of knots, and weighting techniq ue. These depend upon the structure of the data. However, higher order spli nes are not recommended since the result might become extremely unstable. T he 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 multiv ariate approach.