Uniform convergence of local Fréchet regression with applications to locating extrema and time warping for metric space valued trajectories

Local Fréchet regression is a nonparametric method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general spaces from noisy random objects. We derive uniform rates convergence, so far have eluded theoretical analysis this method, both fixed target trajectories, where we utilize tools empirical processes. These results are shown widely applicable data analysis. In addition simulations, provide two pertinent examples these important: The consistent estimation the location properly defined extrema illustrate with problem locating age minimum brain connectivity as obtained fMRI data; time warping illustrated yearly age-at-death distributions different countries.