The viewpoint taken in much of this text is that PCA is mainly a descriptive tool with no need
for rigorous distributional or model assumptions. This implies that it can be used on a wide …

Partial least squares regression has been an alternative to ordinary least squares for
handling multicollinearity in several areas of scientific research since the 1960s. It has …

Through the remarkable progress in technology, it is getting easier and easier to generate
vast amounts of variables from a given sample. The selection of variables is imperative for …

We look at the problem of predicting several response variables from the same set of
explanatory variables. The question is how to take advantage of correlations between the …

Motivation: One important application of gene expression microarray data is classification of
samples into categories, such as the type of tumor. The use of microarrays allows …

This chapter reviews methods for selecting empirically relevant predictors from a set of N
potentially relevant ones for the purpose of forecasting a scalar time series. First, criterion …

Beginning with a discussion of RA Fisher's early written remarks that relate to dimension
reduction, this article revisits principal components as a reductive method in regression …

Asset returns change with fundamentals and other factors, such as technical information and
sentiment over time. In modeling time-varying expected returns, this article focuses on the …

With advancing of modern technologies, high-dimensional data have prevailed in
computational biology. The number of variables p is very large, and in many applications, p …

We give a survey of partial least squares regression with one y variable from a theoretical
point of view. Some general comments are made on the motivation as seen by a statistician …