1962/09/01 by J. S. Williams · 12 citations
Mathematics · Chemistry · #Advanced Statistical Methods and Models #Statistical Methods and Applications #Spectroscopy and Chemometric Analyses
paper · doi:10.2307/2527479
The coefficients in both linear functions (aj and cj) are known constants. Smith's solution is in terms of the population parameters of gq and ej, which in practice must be estimated from sample data. For more than two variates, these estimates are laborious to calculate and in small samples possess very complicated statistical properties. It has been shown by Williams [1961, 1962] that, for the assumption of normal additive vectors gi = gqj and ej = eii, some of the estimated weights have finite variances only if the number of classes used to estimate the covariances of the qij exceeds by five or more the number of variates included in the index, and that failure to correct the index weights for a bias factor can result in a negative correlation of the index with true worth. These difficulties prompt the following questions. Has the selection index constructed with sample estimates of the population parameters been proven reliable enough to merit its use? Would an index, such as a linear combination of the observable variates using the known weights of the nonobservable linear functions, be