One component partial least squares, high dimensional regression, data splitting, and the multitude of models

David J. Olive and Lingling Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 1, 130-145

Abstract: This article gives large sample theory for the one component partial least squares estimator, including some hypothesis tests for high dimensional data, under much weaker conditions than those in the literature. Simple theory is also given for some data splitting estimators and the marginal maximum likelihood estimators. It is shown that lasso, one component partial least squares, and ordinary least squares often estimate different population multiple linear regression models. The article also proves that there are often many valid population models for regression methods such as binary regression.

Date: 2025
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DOI: 10.1080/03610926.2024.2303979

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