Byeong U. Park

My current research areas include non- and semi-parametric inference on structured models for non-Euclidean data and its applications in various scientific domains. Non-Euclidean data are encountered everywhere due to the modern technology of data collection. Functional, compositional, spherical, shape and special-orthogonal-matrix-valued data, among others, are important examples of non-Euclidean data. Functional data refer to a collection of observed random functions that correspond to smooth realizations of an underlying stochastic process. Compositional data arise from numerous sources such as elections, compositions of body, air, sea-water, soil and income-expenditure distributions, etc. Spherical data, with circular data as a special case, emerge from earth science and astronomy, for example, such as the directions of wind and animal movement, and the positions of sunspots and airplanes, etc. A shape value is a set of finite points representing the shape of an artificial or natural object. Examples are shapes of skulls, organs, faces, sand-particles and lands. Some examples of special-orthogonal-matrix-valued data include vector-cardiograms and alignments of crystals. Non- and semi-parametric structured models are extremely useful statistical tools that can be used in a variety of modern real applications. They possess flexibility of nonparametric models, and at the same time circumvent very efficiently the curse of dimensionality of nonparametric models. There have been only a few attempts to develop methodology and related theory for these models that are applicable to non-Euclidean data. The case with ultra-high-dimensional data in the framework of nonparametric structured models is also in an opening stage. I am conducting comprehensive research on analyzing non-Euclidean and high-dimensional data based on nonparametric structured models.