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Guy Martial Nkiet

Publications and source records attributed to Guy Martial Nkiet.

At least 19 recordsLinked to original sources
arXiv2026

Testing for point-impact effects in a spatial semi-functional linear regression model

This paper introduces a novel semiparametric testing framework for localized point-impact effects within a spatial semi-functional linear regression model. We address an intricate inferential problem that simultaneously accommodates three distinct sources of complexity: an infinite-dimensional global functional slope, an unknown smooth spatial nuisance surface, and data-dependent, unobserved impact locations. To isolate the point-impact coefficients, we construct a robust residualized cross-moment estimator after regularizing the functional component via Tikhonov inverse and estimating the spatial nuisance surface through local-linear smoothing. We establish a multivariate central limit theorem under the null hypothesis of no point-impact effect. We develop two operational test statistics: a general formulation whitened by the long-run covariance matrix to handle arbitrary spatial dependence, and a simpler chi-square calibration valid under short-range spatial dependencies in regression errors. Rigorous finite-sample simulations and an application to Canadian weather data demonstrate the superior power and size control of our methodology.

stat.ME↗
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

Testing for homogeneity of several functional variables via multiple maximum variance discrepancy

This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance discrepancy (MMVD). Then, a consistent estimator of this measure is proposed as test statistic, and its asymptotic distribution under the null hypothesis is derived. A simulation study comparing the proposed test with existing ones is provided

math.ST↗
arXiv2023

A method for variable selection in a multivariate functional linear regression model

We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients that lead to a multivariate linear regression model. Then a criterion by means of which the variable selection problem reduces to that of estimating a suitable set is introduced. Estimation of this set is achieved by using appropriate penalizations of estimates of this criterion, so leading to our proposal. A simulation study that permits to investigate the effectiveness of the proposed approach and to compare it with existing methods is given.

math.ST↗
arXiv2023

Variable selection in multivariate regression model for spatially dependent data

This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in $\mathbb{Z}^d$ with $d\geqslant 2$. We use a criterion that allows to characterize the subset of relevant variables as depending on two parameters, and we propose estimators for these parameters based on spatially dependent observations. We prove the consistency, under specified assumptions, of the method thus proposed. A simulation study made in order to assess the finite-sample behaviour of the proposed method with comparison to existing ones is presented.

math.ST↗
arXiv2022

On estimation and prediction in a spatial semi-functional linear regression model

We tackle estimation and prediction at non-visted sites in a spatial semi-functional linear regression model with derivatives that combines a functional linear model with a nonparametric regression one. The parametric part is estimated by a method of moments and the other one by a local linear estimator. We establish the convergence rate of the resulting estimators and predictor. A simulation study and an application to ozone pollution prediction at non-visted sites are proposed to illustrate our results.

math.ST↗
arXiv2022

An independence test for functional variables based on kernel normalized cross-covariance operator

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized cross-covariance operator. We then get asymptotic normality of this statistic under independence hypothesis, so leading to a new test for independence of functional random variables. A simulation study that allows to compare the proposed test to existing ones is provided.

math.ST↗
arXiv2022

Kernel-based method for joint independence of functional variables

This work investigates the problem of testing whether $d$ functional random variables are jointly independent using a modified estimator of the $d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes HSIC for the case where $d \geq 2$. We then get asymptotic normality of this estimator both under joint independence hypothesis and under the alternative hypothesis. A simulation study shows good performance of the proposed test on finite sample.

math.ST↗
arXiv2022

Asymptotic normality of an estimator of kernel-based conditional mean dependence measure

We propose an estimator of the kernel-based conditional mean dependence measure obtained from an appropriate modification of a naive estimator based on usual empirical estimators. We then get asymptotic normality of this estimator both under conditional mean independence hypothesis and under the alternative hypothesis. A new test for conditional mean independence of random variables valued into Hilbert spaces is then introduced.

math.ST↗
arXiv2022

Testing independence of functional variables by an Hilbert-Schmidt independence criterion estimator

We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the alternative hypothesis. A new test for independence of random variables valued into metric spaces is then introduced, and a simulation study that allows to compare the proposed test to an existing one is provided

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↗
arXiv2020

Asymptotic normality of a generalized maximum mean discrepancy estimator

In this paper, we propose an estimator of the generalized maximum mean discrepancy between several distributions, constructed by modifying a naive estimator. Asymptotic normality is obtained for this estimator both under equality of these distributions and under the alternative hypothesis.

math.ST↗
arXiv2019

Robustifying multiple-set linear canonical analysis with S-estimator

We consider a robust version of multiple-set linear canonical analysis obtained by using a S-estimator of covariance operator. The related influence functions are derived. Asymptotic properties of this robust method are obtained and a robust test for mutual non-correlation is introduced.

math.ST↗
arXiv2019

Dimension reduction in spatial regression with kernel SAVE method

We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the interest matrix and the effective dimension reduction (EDR) space, and show their consistency.

math.ST↗
arXiv2019

On estimation and prediction in spatial functional linear regression model

We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample bound for variance of this estimator under mixing spatial dependence. Then, we give a bound of the prediction error. Finally, we illustrate our results by simulations

math.ST↗
arXiv2018

Kernel based method for the $k$-sample problem

In this paper we deal with the problem of testing for the equality of $k$ probability distributions defined on $(\mathcal{X},\mathcal{B})$, where $\mathcal{X}$ is a metric space and $\mathcal{B}$ is the corresponding Borel $σ$-field. We introduce a test statistic based on reproducing kernel Hilbert space embeddings and derive its asymptotic distribution under the null hypothesis. Simulations show that the introduced procedure outperforms known methods.

math.ST↗
arXiv2018

$k$-Sample problem based on generalized maximum mean discrepancy

In this paper we deal with the problem of testing for the quality of $k$ probability distributions. We introduce a generalization of the maximum mean discrepancy that permits to characterize the null hypothesis. Then, an estimator of it is proposed as test statistic, and its asymptotic distribution under the null hypothesis is derived. Simulations show that the introduced procedure outperforms classical ones.

math.ST↗