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<p>The relationship between temperature and electricity consumption may vary with household wealth, highlighting a critical issue of inequality in energy usage. To address this, we propose a Generalized Functional Additive Nonlinear Model with Multimodal Interaction effects (FANMI), which leverages Functional Principal Component Analysis (FPCA) to capture the complex interplay between functional and scalar covariates—referred to here as multimodal interaction. Our estimation procedure combines quasi-likelihood methods with B-spline approximation to efficiently fit the FANMI model. We establish the optimal convergence rate and derive the asymptotic normality of the resulting estimators. Furthermore, we develop two hypothesis testing procedures: one to evaluate the overall goodness-of-fit of the FANMI model, and another to test whether certain bivariate nonparametric interaction functions can be simplified to univariate forms. The asymptotic distributions of the proposed test statistics are also derived. Extensive simulation studies are conducted to assess the finite-sample performance of both the estimation and testing methods. Finally, we illustrate the practical utility of FANMI by analyzing the joint effects of temperature and GDP on electricity consumption and the electricity Gini coefficient.</p>

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Generalized functional additive nonlinear models with multimodal interaction effects

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Jiaqi Men,
  • Hua Liu,
  • Jinhong You,
  • Xin Chen,
  • Jiguo Cao

摘要

The relationship between temperature and electricity consumption may vary with household wealth, highlighting a critical issue of inequality in energy usage. To address this, we propose a Generalized Functional Additive Nonlinear Model with Multimodal Interaction effects (FANMI), which leverages Functional Principal Component Analysis (FPCA) to capture the complex interplay between functional and scalar covariates—referred to here as multimodal interaction. Our estimation procedure combines quasi-likelihood methods with B-spline approximation to efficiently fit the FANMI model. We establish the optimal convergence rate and derive the asymptotic normality of the resulting estimators. Furthermore, we develop two hypothesis testing procedures: one to evaluate the overall goodness-of-fit of the FANMI model, and another to test whether certain bivariate nonparametric interaction functions can be simplified to univariate forms. The asymptotic distributions of the proposed test statistics are also derived. Extensive simulation studies are conducted to assess the finite-sample performance of both the estimation and testing methods. Finally, we illustrate the practical utility of FANMI by analyzing the joint effects of temperature and GDP on electricity consumption and the electricity Gini coefficient.