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<p>The varying coefficient model mitigates the curse of dimensionality in nonparametric regression as the number of explanatory variables increases. To address high-dimensional uncertain phenomena characterized by imprecise observations, this paper introduces two uncertain varying coefficient models, employing uncertain variables for robust modeling. Based on the least squares method, we use local linear and B-spline estimations for the two models with crisp and uncertain explanatory variables. To account for potential differences in smoothness among various coefficient functions, we propose two-step estimation procedures based on the two approaches to improve the fitting accuracy. In addition, residual analysis and uncertain hypothesis testing are performed to evaluate the suitability of the fitted model. Two numerical examples and an application involving weather data demonstrate the effectiveness of these methods.</p>

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Estimation problems in two types of uncertain varying coefficient models with imprecise observations

  • 期刊论文

  • 发表日期：

    2025年4月12日

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  • Yuxuan Zhang,
  • Zhiming Li

摘要

The varying coefficient model mitigates the curse of dimensionality in nonparametric regression as the number of explanatory variables increases. To address high-dimensional uncertain phenomena characterized by imprecise observations, this paper introduces two uncertain varying coefficient models, employing uncertain variables for robust modeling. Based on the least squares method, we use local linear and B-spline estimations for the two models with crisp and uncertain explanatory variables. To account for potential differences in smoothness among various coefficient functions, we propose two-step estimation procedures based on the two approaches to improve the fitting accuracy. In addition, residual analysis and uncertain hypothesis testing are performed to evaluate the suitability of the fitted model. Two numerical examples and an application involving weather data demonstrate the effectiveness of these methods.