When is the inverse regression estimator MSE-superior to the standard regression estimator in multivariate controlled calibration situations?

We assume as model a standard multivariate regression of y on x, fitted to a controlled calibration sample and used to estimate unknown x′s from observed y-values. The standard weighted least squares estimator (‘classical’, regress y on x and ‘solve’ for x) and the biased inverse regression estimator (regress x on y) are compared with respect to mean squared error. The regions are derived where the inverse regression estimator yields the smaller MSE. For any particular component of x this region is likely to contain ‘most’ future values in usual practice. For simultaneous estimation this needs not be true, however.     

Beiträge zur Chemie der Schwefelhalogenide. 11. UV/VIS-spektroskopische Untersuchung Über die Existenz von CF3S(O)I und das Schwingungsspektrum von CF3S(O)Br

Contribution to the Chemistry of Sulfur Halides. 11. UV/VIS Spectroscopic Investigations on the Existence of CF₃S(O)I and the Vibrational Spectrum of CF₃S(O)Br The very instable compound CF₃S(O)I is identified by correlating its UV/VIS absorptions (245, 310, 340 nm) with those of the homologous trifluoromethylsulfinylhalides and by the decomposition products. The assigned vibrational spectrum of CF₃S(O)Br is given.