Olive, DavidAlshammari, Abdulaziz2024-07-172024-07-172024-05-28https://hdl.handle.net/20.500.14154/72619We derive some large sample theory for the marginal maximum likelihood estimator for multiple linear regression. Then testing is considered for that estimator and the one component partial least squares estimator, including some high dimensional tests. Testing with these two estimators for the multiple linear regression model with heterogeneity and for the single index model is also considered.85en-USData splittingdimension reductionhigh dimensional datalassosingle index model.Thesis