Order restricted univariate and multivariate inference with adjustment for covariates in partially linear models

In a variety of applications researchers are interested in comparing two or more naturally ordered experimental conditions after adjusting for covariates. Addressing this problem we develop a methodology for estimating a mean response conditional on covariates in the framework of partially linear models which allows the effects of some covariates to be modeled nonparametrically. Our focus is on univariate responses but extensions to multivariate response data are also considered. The new methodology is applied to data from a study that examined the relationship between exposure to PFASs, a class of widely used environmental pollutants, and plasma lipids in a cohort of pregnant women.