## On the Grenander estimator at zero.(English)Zbl 1214.62037

Summary: We establish limit theory for the Grenander estimator of a monotone density near zero. In particular we consider the situation when the true density $$f_0$$ is unbounded at zero, with different rates of growth to infinity. In the course of our study we develop new switching relations using tools from convex analysis. The theory is applied to a problem involving mixtures.

### MSC:

 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 52A99 General convexity
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