A1082
Title: Nonlinear global Frechet regression for random objects via weak conditional expectation
Authors: Bing Li - The Pennsylvania State University (United States) [presenting]
Abstract: The notion of a weak conditional Frechet mean is introduced based on Carleman operators, and then a global nonlinear Frechet regression model is proposed by reproducing kernel Hilbert space (RKHS) embedding. Furthermore, the relationships between the conditional Frechet mean and the weak conditional Frechet mean are established for both Euclidean and object-valued data. The state-of-the-art global Frechet regression is shown to emerge as a special case of the method by choosing a linear kernel. The metric space is required for the predictor to admit a reproducing kernel, while the intrinsic geometry of the metric space for the response is utilized to study the asymptotic properties of the proposed estimates. Numerical studies, including extensive simulations and a real application, are conducted to investigate the performance of the estimator in a finite sample.
