Gross error sensitivity

Occasionally it is convenient to refer to the p function in (11.21), but generally the form (11.22) is used in robust M-estimation. The use of the t(r form is due to Hampel s concept of the influence function (Hampel et al., 1986). According to the IF concept, the value of it represents the effect of the residuals on the parameter estimation. If iff is unbounded, it means that an outlier has an infinite effect on the estimation. Thus, the most important requirement for robustness is that iff must be bounded and should have a small value when the residual is large. In fact, the value of the iff function corresponds to the gross error sensitivity (Hampel etal., 1986), which measures the worst (approximate) influence that a small amount of contamination of fixed size can have on the value of the estimator. 

Unlike the other two tests, this is associated with each measurement. Reconcihation is required before this test is apphed, but no further isolation is required. However, due to the limitations in reconciliation methods, some measurements can be inordinately adjusted because of incorrectly specified random errors. Other adjustments that do contain gross errors may not be adjusted because the selected constraints are not sensitive to these measurements. Therefore, even though the adjustment in each measurement is tested for gross error, rejection of the mill hypothesis for a specific measurement does not necessarily indicate that that measurement contains gross error. 

Although well designed LC-MS/MS assays generally outperform immunoassays due to their accuracy, sensitivity, precision, and inherent multiplexing capability, they are not free from analytical problems. Besides limitations in selectivity— isobaric analytes cannot be distinguished—sudden and unpredictable ion yield attenuations, often known as ion suppression effect, have to be considered the Achilles heel of quantitative bio-analytical mass spectrometry. Ion yield attenuation is compromising both the accuracy of an assay and its precision. It can easily lead to gross errors in analyte quantification. 

Older methods based on solubility changes upon complexation, or on partition coefficients between aqueous solutions and hydrophobic solvents, have been shown to lead to gross errors as compared to spectroscopic techniques (40) that are also less sensitive to the formation of emulsions, micelles, and so on. The traditional X-ray analysis of inclusion compounds is of limited significance for establishing complexation between lipophilic substrates and macrocyclic host, particularly in aqueous solution. The essential hydrophobic driving force for complexation, of course, is nonexistent in the crystal. The future development of NMR methods including shielding calculations and measurements of intermolecular nuclear Overhauser effects is expected to provide the most reliable information on intercavity inclusion complexes in solution as the basis for catalytic applications. 

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