A selective review on conditional density estimation

Conditional density estimation is a fundamental research problem in data science, naturally arising in a variety of applications such as semiparametric statistics, causal inference and machine learning. However, methodology development for conditional density estimation has received rather limited attention, in particular in comparison with conditional expectation estimation. In this review paper, we survey available nonparametric methods, as well as their corresponding software, in the literature for conditional density estimation. Specifically, we focus on nonparametric methods based on kernel smoothing, orthogonal basis expansion, and a highly adaptive lasso estimation strategy. We compare numerical performance of these methods in a comprehensive simulation study as well as in three benchmark data sets.

Keywords

conditional density estimation, kernel smoothing, orthogonal basis expansion, highly adaptive lasso estimation

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Received 29 November 2022

Accepted 3 September 2023

Published 19 July 2024