Theil–Sen nonparametric regression technique on univariate calibration, inverse regression and detection limits

This paper reports the combined use of the nonparametric Theil–Sen (TS) regression technique and of the statistics of Lancaster–Quade (LQ) concerning the linear regression parameters to solve typical analytical problems, like method comparison, calculation of the uncertainty in the inverse regression, determination of the detection limit. The results of this new approach are compared to those obtained with appropriate reference methods, using simulated and real data sets. The nonparametric Theil–Sen regression technique appears a new robust tool for the problems considered because it is free from restrictive statistical constraints, avoids searching for the error nature on x and y, which may require long analysis times, and it is easy to use. The only drawback is that the intrinsic nature of the method may lead to a possible enlargement of the uncertainty interval of the discriminated concentration and to the determination of larger detection limits than those obtainable with the commonly used, less robust, regression techniques.