University of California, Davis
In this talk, I will first present a method for conditional distribution and quantile estimation when predictors take values in a functional space, which is an extension of the usual functional mean regression. The study is motivated and illustrated by an application to the assessment of children’s growth patterns. The proposed method is supported by theory and is shown to perform well in simulations. An extension of the proposed conditional approach to model the more complex case when responses are also functions will be briefly discussed. In the second part, I will adopt a broader perspective, and demonstrate how the ‘blessings of dimensionality’ principle motivates the `Stringing’ method. In this approach, we represent high-dimensional data as discretized, noisy, and order-scrambled observations from a hidden stochastic process. Simulations show that this method works well in various high-dimensional settings.