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# Michael Nussbaum

Professor

### Departments/Programs

- Mathematics

### Graduate Fields

- Mathematics
- Statistics

## Research

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. Current efforts concentrate on models of dependent observations, such as stationary or locally stationary Gaussian sequences, with high or infinite dimensional parameter space.

However I am also interested in unsolved problems in the simple signal-plus-noise setting, such as sharp error asymptotics for adaptive nonparametric hypothesis testing.

Another line of research is quantum statistics, a field connected to recent technological progress in quantum computing and communication. Here the emphasis is on results for hypothesis testing and discrimination between quantum states, such as the quantum Chernoff bound.

## Courses

## Publications

- An asymptotic error bound for testing multiple quantum hypotheses (with A. Szkoła), Ann. Statist. 39 (2011), 3211–3233
- Asymptotic equivalence of spectral density estimation and Gaussian white noise (with G. K. Golubev and H. H. Zhou), Ann. Statist. 38 (2010), 181-214
- The Chernoff lower bound for symmetric quantum hypothesis testing (with A. Szkoła), Ann. Statist. 37 (2009), 1040-1057
- Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift (with V. Genon-Catalot and C. Larédo), Ann. Statist. (2002), 30 731-753
- Diffusion limits for nonparametric autoregression (with G. Milstein). Probab. Theory Related Fields 112 (1998), 535-543
- Asymptotic equivalence of density estimation and Gaussian white noise, Ann. Statist. 24 (1996), 2399-2430