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Dimension Reduction in High-Dimensional Regression Methods

High-dimensional statistics has been the focus point of manystatisticians all over the world, because of its many attractive applicationsin various fields. Since traditional statistical tools do not work forhigh-dimensional statistics, the use of statistical methodology in the analysisof high-dimensional data, specially related to supervised regression (modelselection, estimation and prediction) and multivariate techniques (principlecomponents, partial least square and cluster analysis), has beengrowing. Principle Component Regression (PCR) and Partial Least SquareRegression (PLSR) are methods concerned with explaining the variance-covariance structure of data through a smallnumber of components which are linear combinations of the original variables. Least Absolute Shrinkage and SelectionOperator (LASSO) has become popular for high-dimensional estimation problems,having statistical accuracy for prediction and variable selection. One of the objectives ofthese methods are data reduction.

In this work, we will discuss about PCR, PLSR and LASSO with anapplication in a high-dimensional data set.

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