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Partially Linear Additive Regression with a General Hilbertian Response

Author

Listed:
  • Sungho Cho
  • Jeong Min Jeon
  • Dongwoo Kim
  • Kyusang Yu
  • Byeong U. Park

Abstract

In this article we develop semiparametric regression techniques for fitting partially linear additive models. The methods are for a general Hilbert-space-valued response. They use a powerful technique of additive regression in profiling out the additive nonparametric components of the models, which necessarily involves additive regression of the nonadditive effects of covariates. We show that the estimators of the parametric components are n-consistent and asymptotically Gaussian under weak conditions. We also prove that the estimators of the nonparametric components, which are random elements taking values in a space of Hilbert-space-valued maps, achieve the univariate rate of convergence regardless of the dimension of covariates. We present some numerical evidence for the success of the proposed method and discuss real data applications. Supplementary materials for this article are available online.

Suggested Citation

  • Sungho Cho & Jeong Min Jeon & Dongwoo Kim & Kyusang Yu & Byeong U. Park, 2024. "Partially Linear Additive Regression with a General Hilbertian Response," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 942-956, April.
    • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:546:p:942-956
    DOI: 10.1080/01621459.2022.2149407
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