Two-stage conditional density estimation based on Bernstein polynomials

Mohamed Belalia and Guanjie Lyu

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 11, 4172-4193

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.

Date: 2024
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DOI: 10.1080/03610926.2023.2176715

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