To compare their performance on high dimensional data, several regression methods are applied to data sets in which the number of exploratory variables greatly exceeds the sample sizes. The methods are stepwise regression, principal components regression, two forms of latent root regression, partial least squares, and a new method developed here. The data are four sample sets for which near infrared reflectance spectra have been determined and the regression methods use the spectra to estimate the concentration of various chemical constituents, the latter having been determined by standard chemical analysis. Thirty-two regression equations are estimated using each method and their performances are evaluated using validation data sets. Although it is the most widely used, stepwise regression was decidedly poorer than the other methods considered. Differences between the latter were small with partial least squares performing slightly better than other methods under all criteria examined, albeit not by a statistically significant amount.
Abstract Partial least squares (PLS) regression ( a.k.a. projection on latent structures) is a recent technique that combines features from and generalizes principal component a...
Summary Various topics are reviewed: the effect of modern computers on statistical calculation; analysis by vector components rather than analysis merely of variance; “stepwise ...
In this paper a modification of the standard algorithm for non-negativity-constrained linear least squares regression is proposed. The algorithm is specifically designed for use...
The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal re...
Abstract In this paper a general algorithm is provided for maximum likelihood fitting of deterministic models subject to Gaussian‐distributed residual variation (including any t...
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