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arXiv · 2609.30161

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

Stéphane Bouka·Emmanuel De Dieu Nkou·Alban Mbina Mbina·Guy Martial Nkiet
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Abstract

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.

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Stéphane Bouka, Emmanuel De Dieu Nkou, Alban Mbina Mbina, Guy Martial Nkiet. 2026-09-24. Testing for point-impact effects in a spatial semi-functional linear regression model. https://arxiv.org/abs/2609.30161

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