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arXiv · 2505.19359

Nonparametric estimation of sliced inverse regression by the $ k$-nearest neighbors kernel method

Luran Bengono Mintogo·Emmanuel de Dieu Nkou·Guy Martial Nkiet
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Abstract

We investigate nonparametric estimation of sliced inverse regression (SIR) via the $k$-nearest neighbors approach with a kernel. An estimator of the covariance matrix of the conditional expectation of the explanatory random vector given the response is then introduced, thereby allowing to estimate the effective dimension reduction (EDR) space. Consistency of the proposed estimators is proved through derivation of asymptotic normality. A simulation study, made in order to assess the finite-sample behaviour of the proposed method and to compare it to the kernel estimate, is presented.

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Luran Bengono Mintogo, Emmanuel de Dieu Nkou, Guy Martial Nkiet. 2025-05-25. Nonparametric estimation of sliced inverse regression by the $ k$-nearest neighbors kernel method. https://arxiv.org/abs/2505.19359

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