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

Area of Science:

• Analytical Chemistry
• Statistical Modeling

Background:

• Traditional regression methods in analytical chemistry often involve complex statistical assumptions and can be time-consuming.
• Accurate determination of method comparison, inverse regression uncertainty, and detection limits are crucial in analytical problem-solving.

Purpose of the Study:

• To evaluate the combined application of Theil-Sen (TS) regression and Lancaster-Quade (LQ) statistics for analytical problems.
• To assess the robustness and efficiency of this novel approach compared to existing methods.

Main Methods:

• Utilized the nonparametric Theil-Sen (TS) regression technique combined with Lancaster-Quade (LQ) statistics.
• Applied the approach to analytical challenges including method comparison, inverse regression uncertainty, and detection limit determination.
• Validated results using both simulated and real-world data sets, comparing them against established reference methods.

Main Results:

• The Theil-Sen (TS) regression technique demonstrated robustness and ease of use, free from restrictive statistical constraints.
• This method simplifies analytical procedures by avoiding the need to determine error distributions on both x and y variables.
• A potential drawback identified is a possible enlargement of the uncertainty interval for discriminated concentration and higher detection limits compared to less robust techniques.

Conclusions:

• The combined TS and LQ approach offers a robust and efficient alternative for common analytical problems in chemistry.
• Its non-parametric nature and simplified error handling make it a valuable tool, despite potential trade-offs in uncertainty and detection limits.
• Further investigation into optimizing TS regression for specific analytical applications is warranted.