Asymptotic distribution of one-component partial least squares regression estimators in high dimensions

Abstract

In a one-component partial least squares fit of a linear regression model, we find the asymptotic normal distribution, as the sample size and number of predictors approach infinity, of a user-selected univariate linear combination of the coefficient estimator and give corresponding asymptotic confidence and prediction intervals. Simulation studies and an analysis of a dopamine dataset are used to support our theoretical asymptotic results and their practical application.