<ul data-eligibleForWebStory="false"><li>Regressing a function on multidimensional space without the issues of statistical and computational complexity requires specific statistical models.</li><li>Compositional models involving a composition of functions, particularly when one function is nonlinear, are less explored in the context of avoiding the curse of dimensionality.</li><li>A proposed nonlinear model involves projecting data onto a regular curve parameter and applying a function, serving as a nonlinear extension of the single-index model.</li><li>A nonparametric conditional regression estimator for this model, under certain assumptions like coarse monotonicity, achieves close to optimal rates for non-parametric regression and can be implemented efficiently.</li></ul>

Conditional regression for the Nonlinear Single-Variable Model

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