arXiv subjects

Emmanuel de Dieu Nkou

Publications and source records attributed to Emmanuel de Dieu Nkou.

3 recordsLinked to original sources

arXiv2025

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

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.

math.ST↗

arXiv2024

Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function

We adress the problem of consistency of the $k$-nearest neighbors kernel estimators of the density and the regression function in the multivariate case. We get the rates of strong uniform consistency on the whole space $\mathbb{R}^p$ for these estimators under specified assumptions.

math.ST↗

arXiv2020

Wavelet-based estimation in a semiparametric regression model

In this paper, we introduce a wavelet-based method for estimating the EDR space in Li's semiparametric regression model for achieving dimension reduction. This method is obtained by using linear wavelet estimators of the density and regression functions that are involved in the covariance matrix of conditional expectation whose spectral analysis gives the EDR directions. Then, consistency of the proposed estimators is proved. A simulation study that allow one to evaluate the performance of the proposal with comparison to existing methods is presented.

math.ST↗