55 research outputs found
Contraction and uniform convergence of isotonic regression
We consider the problem of isotonic regression, where the underlying signal
is assumed to satisfy a monotonicity constraint, that is, lies in the
cone . We study the isotonic
projection operator (projection to this cone), and find a necessary and
sufficient condition characterizing all norms with respect to which this
projection is contractive. This enables a simple and non-asymptotic analysis of
the convergence properties of isotonic regression, yielding uniform confidence
bands that adapt to the local Lipschitz properties of the signal
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