Abstract: We propose a partially-global Fréchet regression model by extending the profiling technique for the partially linear regression model (Severini and Wong, 1992). This extension allows for the response to come from a generic metric space and can incorporate a combination of Euclidean predictors and a predictor which comes from another generic metric space. By melding together the local and global Fréchet regression models proposed by Petersen and Müller (2019), we gain a model that is more flexible than global Fréchet regression and more accurate than local Fréchet regression when the data generating process relies on a non-Euclidean predictor or is truly "global (linear)" for some scalar predictors. In this paper, we provide theoretical support for partially-global Fréchet regression and demonstrate its competitive finite-sample performance when applied to both simulated data and to real data which is too complex for traditional statistical methods.

Key words and phrases: Fréchet regression, local polynomial smoothing, non-Euclidean predictor, non-Euclidean response, partially linear model.