Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels

The relationship between conditional expected returns, conditional risk, and asset characteristics has been a central topic in financial economics for decades. Yet, inference in this domain remains constrained by the unbalanced and high-dimensional nature of real-world data. In this paper, we address these challenges by introducing a nonparametric, kernelbased framework for the joint estimation of conditional mean and covariance matrices, providing a powerful and tractable solution to the econometric inference problem highlighted by Cochrane (2011). Our framework is specifically designed to deliver positive semidefinite covariance matrices across any state and for cross sections of varying sizes, filling a significant gap in the literature.