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Density estimation and conditional density estimation via a least squares reconstruction method

Author

Listed:
  • Siyuan Huang

    (Beijing University of Technology, School of Mathematics, Statistics and Mechanics)

  • Shifeng Xiong

    (Chinese Academy of Sciences, NCMIS, KLSC, Academy of Mathematics and Systems Science
    University of Chinese Academy of Sciences, School of Mathematical Sciences)

  • Tianfa Xie

    (Beijing University of Technology, School of Mathematics, Statistics and Mechanics)

Abstract

Density estimation and conditional density estimation are fundamental problems in statistics. In this paper, we propose the least squares reconstruction density estimation (LSRDE) method for density estimation, which combines least squares density estimation and reconstruction parameterization. The main advantage of the proposed method is its analytic form, which makes it suitable for massive data analysis. LSRDE is extended to the conditional density estimation, and we refer to the method as the least squares reconstruction conditional density estimation (LSRCDE). Numerical experiments show that LSRDE and LSRCDE are very competitive.

Suggested Citation

  • Siyuan Huang & Shifeng Xiong & Tianfa Xie, 2026. "Density estimation and conditional density estimation via a least squares reconstruction method," Computational Statistics, Springer, vol. 41(4), pages 1-29, June.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:4:d:10.1007_s00180-026-01752-4
    DOI: 10.1007/s00180-026-01752-4
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