Optimal Kernel for Kernel-Based Modal Statistical Methods
This work addresses a specific theoretical bottleneck in statistical estimation, but it appears incremental as it focuses on optimizing within an existing framework.
The authors tackled the problem of kernel selection in kernel-based modal statistical methods, theoretically deriving an optimal multivariate kernel that minimizes asymptotic error when using an optimal bandwidth.
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to the estimation accuracy of these methods. In particular, we theoretically show a (multivariate) optimal kernel that minimizes its analytically-obtained asymptotic error criterion when using an optimal bandwidth, among a certain kernel class defined via the number of its sign changes.