Past lectures

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Abstract

Many nonparametric estimators which arise as solutions of optimization problems (maximum likelihood, least squares, etc.) have non-normal limit distributions, and converge at rates slower than n−1/2. This type of limit behavior is commonly called ”non-standard asymptotics”, and the local limit often has a characterization in terms a stationary point process. The latter was shown, for example, in [10] for the Grenander estimator of a decreasing density.

Results of this type have counterparts in the theory of interacting particle systems on the integers, such as TASEP (totally asymmetric simple exclusion processes) and in the theory of interacting particle systems on the real line, such as Hammersley’s process. The connection between these seemingly unrelated fields is discussed in [4] for Hammersley’s process, with a follow-up for TASEP in [3]. It is my intention to discuss recent results on these matters and to explore the rather fascinating connection between the fields further during the course. I will also discuss the (many) open problems.