There is currently no well-defined procedure for providing the limit of detection (LOD) in multivariate calibration. Defining an estimator for the LOD in this scenario has shown to be more complex than intuitively extending the traditional univariate definition. For these reasons, although many attempts have been made to arrive at a reasonable convention, additional effort is required to achieve full agreement between the univariate and multivariate LOD definitions. In this work, a novel approach is presented to estimate the LOD in partial least-squares (PLS) calibration. Instead of a single LOD value, an interval of LODs is provided, which depends on the variation of the background composition in the calibration space. This is in contrast with previously proposed univariate extensions of the LOD concept. With the present definition, the LOD interval becomes a parameter characterizing the overall PLS calibration model, and not each test sample in particular, as has been proposed in the past. The new approach takes into account IUPAC official recommendations, and also the latest developments in error-in-variables theory for PLS calibration. Both simulated and real analytical systems have been studied for illustrating the properties of the new LOD concept.

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A new expression is developed which allows estimating the sensitivity for the whole family of multivariate calibration algorithms based on partial least-squares regression combined with residual multilinearization. The sensitivity can be employed to compute other relevant figures of merit such as analytical sensitivity, limit of detection, limit of quantitation, and uncertainty in predicted concentration. The results are substantiated by extensive Monte Carlo noise addition simulations for a variety of systems with a different number of analytes and interfering agents, different degrees of overlapping in component profiles, and different numbers of instrumental data modes per sample, all requiring the achievement of the second-order advantage. The connection between the present approach and the intuitive concept of net analyte signal is discussed. An experimental example for which second-, third-, and fourth-order data are available is also studied, concerning the improvement in figures of merit on increasing the data order, which is consistent with the decrease in average prediction error.