Lipschitz functions decompose into monotonic plus linear parts, yielding sample-split estimators with convergence guarantees under heteroscedastic/heavy-tailed errors and adaptivity to unknown function complexity.
In this case, we perform a coordinate-descent procedure to upd ate ˆgj,L for each j = 1,...d component until the empirical risk converges
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From Isotonic to Lipschitz Regression: A New Interpolative Perspective on Shape-restricted Estimation
Lipschitz functions decompose into monotonic plus linear parts, yielding sample-split estimators with convergence guarantees under heteroscedastic/heavy-tailed errors and adaptivity to unknown function complexity.