Research

Research Area: Mathematical Statistics

My research program focuses on developing a better theoretical understanding of nonparametric statistical inference, using approximations when the sample size is large. A guiding principle is that complicated statistical models should be approximated by simple ones. This can be achieved within the theory of statistical experiments, using the concepts of local asymptotic normality and of Le Cam equivalence. Modern statistical concepts like these are also being integrated into the emerging field of quantum statistics, which is developing on the background of technological breakthroughs in quantum engineering and communication. Here I am currently interested in problems of hypothesis testing and discrimination between quantum states, in connection with the quantum Chernoff bound, and in Gaussian approximation of quantum statistical models. I continue to work on problems in classical nonparametric inference, such as sharp error asymptotics for adaptive nonparametric hypothesis testing.

[Homepage, Michael Nussbaum ]

Supported by National Science Foundation Grant No. DMS- 1407600, *New Horizons in Statistical Decision Theory*

[Project summary | Description | References ]

[ Papers and manuscripts ]: includes publications under the grant and its predecessors since 06/2000.