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Predictive Functional Linear Models with Diverging Number of Semiparametric Single-Index Interactions.

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Summary
This summary is machine-generated.

Including interactions between functional and multivariate predictors improves crop yield prediction. This study develops a semiparametric model to analyze these complex relationships, enhancing prediction accuracy for agricultural applications.

Keywords:
Dimension reductionFunctional data analysisInteractionKernel smoothingSemiparametric

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Area of Science:

  • Statistics
  • Agricultural Science
  • Machine Learning

Background:

  • Accurate crop yield prediction is crucial for food security and agricultural management.
  • Traditional models often struggle to incorporate complex interactions between diverse predictor types.
  • Functional and multivariate data present unique challenges in predictive modeling.

Purpose of the Study:

  • To investigate the benefits of including interaction terms between functional and multivariate predictors for crop yield prediction.
  • To develop and analyze a semiparametric statistical model capable of handling high-dimensional functional data.
  • To establish theoretical properties and practical validation for the proposed modeling approach.

Main Methods:

  • Utilizing functional principal component analysis (FPCA) to reduce the dimensionality of functional predictors.
  • Developing a semiparametric model that incorporates a single-index structure for multivariate predictor interactions.
  • Analyzing the asymptotic properties of the model, including consistency and normality of parametric components.
  • Employing cross-validation (CV) for tuning parameter selection.

Main Results:

  • The inclusion of interactions between functional and multivariate predictors significantly enhances prediction performance.
  • The parametric components of the semiparametric model are shown to be root-n consistent and asymptotically normal.
  • Prediction error is primarily influenced by the estimation of the nonparametric interaction function.
  • A CV-based procedure is validated for effective tuning parameter selection.

Conclusions:

  • The proposed semiparametric approach effectively models interactions between functional and multivariate predictors for improved crop yield prediction.
  • The theoretical analysis provides a strong foundation for the model's statistical properties.
  • The validated CV procedure offers a practical method for implementing the model in real-world agricultural settings.