2,687 research outputs found
Optimal rates and adaptation in the single-index model using aggregation
We want to recover the regression function in the single-index model. Using
an aggregation algorithm with local polynomial estimators, we answer in
particular to the second part of Question~2 from Stone (1982) on the optimal
convergence rate. The procedure constructed here has strong adaptation
properties: it adapts both to the smoothness of the link function and to the
unknown index. Moreover, the procedure locally adapts to the distribution of
the design. We propose new upper bounds for the local polynomial estimator
(which are results of independent interest) that allows a fairly general
design. The behavior of this algorithm is studied through numerical
simulations. In particular, we show empirically that it improves strongly over
empirical risk minimization.Comment: 36 page
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