arXiv subjects

Stéphane Bouka

Publications and source records attributed to Stéphane Bouka.

5 recordsLinked to original sources

arXiv2026

Spatial Functional $k$-Nearest-Neighbour Regression under Polynomial Dependence

This paper investigates non-parametric regression estimation when the explanatory variable takes values in a separable Hilbert space and observations are sampled over an increasing regular spatial lattice. Under a rigorous field-to-field independence setup between covariates and errors, we explore the structural and asymptotic concentration properties of the functional $k$-nearest-neighbour ($k$-NN) estimator. By establishing a sharp pathwise deterministic sandwiching framework for the data-driven random bandwidth, we successfully decouple the local infinite-dimensional small-ball profile from the polynomial covariance decay of the neighborhood indicators. Pointwise convergence rates are derived across short-range, critical, and long-range spatial regimes, revealing a combined penalty term that reflects both covariate spatial interaction and response error memory. Furthermore, uniform consistency over compact subsets is established for unbounded sub-Gaussian error processes through metric entropy and indicator boundary shell chaining. Structured polynomial simulations confirm our theoretical rates and exemplify the precise mechanics of the spatial long-range bottleneck.

math.ST↗

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↗

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↗

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

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