Birgit Grund

A surprising number of real life problems are based on discrete data: they vary from medical diagnosis (Given the yes/no answers of a psychological test, does a certain person need medical help?, or Which treatment is appropriate for different kinds of hip fractures?) to sociological studies (Do male and female high school students have the same opportunities/interests to get a higher education?). Solutions often require reliable density estimates--my main field of research. Density estimation follows the general principle of statistics: Use any information you can get! The basic shape of the density, the number of modes (the more you know), the more efficient you can approximate the true function, provided your information is right! I enjoy investigating nonparametric techniques for both discrete and continuous data. Here we try to avoid any model assumptions and "let the data speak" instead. I like the idea of squeezing out of the data any information you might need, and I am fascinated by the broad variety of creative solutions in this field. Surely, nonparametrics is not the only universal answer to all statistical problems. You have to pay a high price for removing assumptions: serious data-dependent inference requires a large data pool. Particularly in high-dimensional models, the sample size problem is of vital interest. In my current work I focus on kernel estimates for densities and regression curves. I am studying issues such as the interactions of dimension, data sparseness, and smoothness in determining the behavior of kernel estimates; the efficiency of bandwidth choice procedures; methods to decide whether parametric or nonparametric fits should be used.