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This chapter integrates Sparse Principal Component Analysis (SPCA) with High-Dimensional Partially Linear Models using a Local Polynomial Approach to analyze high-dimensional data. By combining SPCA for dimensionality reduction and local polynomial methods for estimating nonlinear relationships, we enhance model interpretability and predictive accuracy. We validate our methodology on a Residential Building Dataset and a DNA Methylation Dataset, applicable to economics, finance, and genomics. Our results show superior performance in Root Mean Squared Error (RMSE) and standard deviation compared to traditional Principal Component Regression and Sparse PCR methods. This advancement improves statistical analysis and broadens the use of semiparametric regression models in various fields.

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Integrating Sparse Principal Component Analysis in High-Dimensional Partially Linear Models: A Local Polynomial Approach

  • 章节

  • 发表日期：

    2025年

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  • Ersin Yilmaz,
  • Dursun Aydin

摘要

This chapter integrates Sparse Principal Component Analysis (SPCA) with High-Dimensional Partially Linear Models using a Local Polynomial Approach to analyze high-dimensional data. By combining SPCA for dimensionality reduction and local polynomial methods for estimating nonlinear relationships, we enhance model interpretability and predictive accuracy. We validate our methodology on a Residential Building Dataset and a DNA Methylation Dataset, applicable to economics, finance, and genomics. Our results show superior performance in Root Mean Squared Error (RMSE) and standard deviation compared to traditional Principal Component Regression and Sparse PCR methods. This advancement improves statistical analysis and broadens the use of semiparametric regression models in various fields.