Discordance between net analyte signal theory and practical multivariate calibration

Area of Science:

• Analytical Chemistry
• Chemometrics

Background:

• Review of Lorber's net analyte signal concept.
• Contextualization within classical and inverse least-squares multivariate calibration.

Purpose of the Study:

• To critically evaluate the relationship between inverse least-squares methods and Lorber's net analyte signal.
• To analyze the impact of device measurement error on calibration procedures.
• To provide theoretical expressions for prediction error metrics.

Main Methods:

• Theoretical analysis of classical and inverse least-squares calibration.
• Examination of multivariate calibration under general measurement error conditions.
• Disproving the approximation of net analyte signal by inverse least-squares methods.

Main Results:

• Classical and inverse calibration exhibit fundamentally different theoretical prediction objectives when measurement error is present.
• The assertion that inverse least-squares procedures approximate the net analyte signal vector is disproved.
• Exact theoretical expressions for prediction error bias, variance, and mean-squared error are derived.

Conclusions:

• Inverse least-squares methods do not approximate Lorber's net analyte signal.
• Significant discrepancies exist between classical, inverse calibration, and net analyte signal theory.
• Implications for multivariate figures of merit and orthogonal projection preprocessing are discussed.