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

BASA, JERÓNIMO; COOK, R. DENNIS; FORZANI, LILIANA; MARCOS, MIGUEL

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE

WILEY-BLACKWELL PUBLISHING, INC

Año: 2022

0319-5724

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.