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

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...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2025-01, Vol.54 (1), p.130-145
Main Authors: J. Olive, David, Zhang, Lingling
Format: Article
Language:English
Subjects:
Cox proportional hazards regression
GLM
Lasso
Maximum likelihood estimators
MMLE
OLS
PLS
Primary 62J05
Regression models
Secondary 62J12
Splitting
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2024.2303979