UC Santa Barbara

In the context of Object oriented data analysis (OODA), the local Fréchet regression was formulated in analogy to the local linear regression to model the conditional Fréchet mean of the response on a single covariate in R. To accommodate p ≥ 2 covariates we introduced the Fréchet single index (FSI) model in analogy to the single index model already existing for responses in R. We discussed the model performance on simulated spherical data and on observed mortality distributions belonging to the L^2-Wasserstein space. We also discussed the consistency of the coefficient vector estimate by combining the Fréchet regression and the M-estimation methods. We discovered the potential of our model to analyze the biomedical data obtained from the wearable accelerometer devices, available for the US population from the NHANES website for the period 2011-14. The physical activity profiles, transformed into quantile distributions, were considered Object responses in the partially linear Fréchet single index (PL-FSI) model which allowed an additive linear part with the single index part. The semi-parametric character of the model allows us to introduce non-linear effects for such covariates as Age, BMI, while theinclusion of a linear part retains the advantage of interpretability for other categorical variables such as diet score, ethnicity, sex and their interaction.