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<p>The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations, which is often unrealistic for spatially structured functional data. We propose a novel penalized spatial function-on-function regression model to address this limitation. Our approach extends the generalized spatial two-stage least-squares estimator to functional data, while incorporating a roughness penalty on the regression coefficient function using a tensor product of B-splines. This penalization ensures optimal smoothness, mitigating overfitting, and improving interpretability. The proposed penalized spatial two-stage least-squares estimator effectively accounts for spatial dependencies, significantly improving estimation accuracy and predictive performance. We establish the asymptotic properties of our estimator, proving its <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sqrt{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msqrt> <mi>n</mi> </msqrt> </math></EquationSource> </InlineEquation>-consistency and asymptotic normality under mild regularity conditions. Extensive Monte Carlo simulations demonstrate the superiority of our method over existing non-penalized estimators, particularly under moderate to strong spatial dependence. In addition, an application to North Dakota weather data illustrates the practical utility of our approach in modeling spatially correlated meteorological variables. Our findings highlight the critical role of penalization in enhancing robustness and efficiency in spatial function-on-function regression models. To implement our method we used the <Emphasis FontCategory="NonProportional">robflreg</Emphasis><InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="MediaObjects/11222_2025_10792_Figa_HTML.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="120" Type="Linedraw" Width="19" /> </InlineMediaObject> package on CRAN.</p>

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Penalized spatial function-on-function regression

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Ufuk Beyaztas,
  • Han Lin Shang,
  • Gizel Bakicierler Sezer

摘要

The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations, which is often unrealistic for spatially structured functional data. We propose a novel penalized spatial function-on-function regression model to address this limitation. Our approach extends the generalized spatial two-stage least-squares estimator to functional data, while incorporating a roughness penalty on the regression coefficient function using a tensor product of B-splines. This penalization ensures optimal smoothness, mitigating overfitting, and improving interpretability. The proposed penalized spatial two-stage least-squares estimator effectively accounts for spatial dependencies, significantly improving estimation accuracy and predictive performance. We establish the asymptotic properties of our estimator, proving its \(\sqrt{n}\) n -consistency and asymptotic normality under mild regularity conditions. Extensive Monte Carlo simulations demonstrate the superiority of our method over existing non-penalized estimators, particularly under moderate to strong spatial dependence. In addition, an application to North Dakota weather data illustrates the practical utility of our approach in modeling spatially correlated meteorological variables. Our findings highlight the critical role of penalization in enhancing robustness and efficiency in spatial function-on-function regression models. To implement our method we used the robflreg package on CRAN.