| Partial least squares regression is a new high-dimension-project-based nonparametric analysis method, which is an extension of ordinal least squares (OLS) to deal with some defects of OLS much more efficiently. Its basic ideals had been come forth in 1960s early. But until 1970s, the NIPALS (nonlinear iterative partial least squares) algorithm had been proposed to realize the ideals of PLS regression. As far as the international workshop on PLS regression had been hold in France in 1990s, it just was the virtual takeoff to develop the theories and applications of PLS rapidly. At present, PLS regression is called the second generation of multivariable statistical analysis by numerous foreign statisticians and has been being used widely in variety of fields, such as chemometrics, industry design, econometrics and so on. However neither theories nor applications of PLS has still attracted a few attentions of native statisticians. In this study, we had paid much attention to PLS regression, included theory, method and application in healthy and medicine researches.We not only introduced the history and current situation of PLS regression by and large, but also extended and proved some basic properties in details. At the same time, several practical algorithms, included NIPALS and SIMPLS, were proposed and their main S AS codes were given in appendices. Through comparing four techniques of outlier test with each other, we summarized their respective advantages and disadvantages of each techniques and clarify the their distinct usages. After gone deep into the ideal and substance of PLS regression, we had proposed a new optimized criterion and applied Monte Carlo randomized simulation to figure out the efficiency of the improvement. The calculation proceedings and result interpretations of PLS regression were illustrated with two examples in healthy and medicine research. And then a series of SAS codes had been provided for the PLS algorithms and the simulation. The main works and results of study are as follows:1. There are a variety of topics on PLS regression, such as its basic ideal, mathematical principles and algorithms, theoretic properties and practical algorithm. On the one hand, when modeling and interpreting our sample data, we generally anticipatedVIIless loss of information in vector spaces, included independent variables space and dependent variables space. On another hand, the maximization of relationship between the two spaces should be up to a certain defined criterion. And we tried to find the appropriate tradeoff among them as well. Obviously this would result in more goodness-of-fit and interpretability of the regression model. Therefore, for the convenience in mathematical expression, we chose such criterion, maximization of covariance, to realize the above ideals. PLS regression simultaneously extracted latent variables (principle components) from the spaces of predictor and response. And then OLS was applied to construct the regression model between them respectively. As a result, three regression functions could be constructed to establish the indirect relationship between the two spaces. We discussed four common outlier tests in PLS regression, included partial F test, residual plot and normal quantile plot, latent variables plot (TIT plot), contribution plot of variables to latent variables. Among these techniques, the first and second are used frequently in ordinal multiple multivariable regression. The third is much common in latent structure analysis. However, the fourth is unique in PLS regression. They define absolutely distinct criteria from various viewpoints to measure the influence of outliers in regression models.2. Based on the basic properties of PLS regression, we had extended and proved a few properties of PLS regression, which distinguished itself from other multivariate statistical analysis. Furthermore, in accordant with the theory of PLS regression, we applied Linear Algebra and Computational Mathematics to establish four practical algorithm of PLS r...
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