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.
Define the resulting estimator for each L as ˆfL(x) = ∑d j=1 ˆgj,L (x) − L⊤ x
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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.