Sparse Variable Sharpening in High-Dimensional Kernel Density Estimation

High-dimensional kernel density estimation suffers from the curse of dimensionality. This study proposes a hybrid density estimator defined as the product of a joint density over a pre-specified subset of dimensions and marginal densities for the remaining variables, instead of estimating the full high-dimensional density directly. Under this framework, given the observed data, we select a subset of variables for joint density construction to improve estimation accuracy, while modeling the remaining variables through their respective marginal densities. This construction involves a trade-off between the approximation error induced by simplifying the dependence structure and the variance reduction achieved by lowering the dimension of the joint density. We employ a genetic algorithm to efficiently identify such variable subsets. Theoretical and numerical results demonstrate that the proposed estimator can outperform conventional full-dimensional kernel density estimation when this trade-off is appropriately balanced.