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Two-stage conditional density estimation based on Bernstein polynomials

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  • Mohamed Belalia
  • Guanjie Lyu

Abstract

Two-stage conditional probability density function estimators are proposed and studied. Specifically, the Nadaraya-Watson (NW) and local linear (LL) conditional distribution function estimators have been smoothed using Bernstein polynomials in the first stage. Second, the proposed estimators are obtained by differentiating NW and LL estimators. The asymptotic properties of these estimators are established such as asymptotic bias, variance, and normality. Finally, a simulation study is carried out to assess the relative advantage of our estimators compared to other competitors. In addition, the well-known Old Faithful Geyser data is analyzed using the proposed estimators.

Suggested Citation

  • Mohamed Belalia & Guanjie Lyu, 2024. "Two-stage conditional density estimation based on Bernstein polynomials," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(11), pages 4172-4193, June.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:11:p:4172-4193
    DOI: 10.1080/03610926.2023.2176715
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