University of Cambridge > > Isaac Newton Institute Seminar Series > Reduced Isotonic Regression

Reduced Isotonic Regression

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact

STSW04 - Future challenges in statistical scalability

Consider an $n$-dimensional vector $X$ with mean $\theta$. In this talk, we consider $\theta$ that is both nondecreasing and has a piecewise constant structure. We establish the exact minimax rate of estimating such monotone functions, and thus give a non-trivial answer to an open problem in the shape-constrained analysis literature. The minimax rate involves an interesting iterated logarithmic dependence on the dimension. We then develop a penalized least-squares procedure for estimating $\theta^*$ adaptively. This estimator is shown to achieve the derived minimax rate without the knowledge of the number of pieces in linear time. We further allow the model to be misspecified and derive oracle inequalities with the optimal rates for the proposed estimator. This is a joint work with Fang Han and Cun-hui Zhang.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2018, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity