Are Non-Gaussian Kernels Suitable for Ensemble Mixture Model Filtering?

In the high-dimensional setting, Gaussian mixture kernel density estimates become increasingly suboptimal. In this work we aim to show that it is practical to instead use the optimal multivariate Epanechnikov kernel. We make use of this optimal Epanechnikov mixture kernel density estimate for the sequential filtering scenario through what we term the ensemble Epanechnikov mixture filter (EnEMF). We provide a practical implementation of the EnEMF that is as cost efficient as the comparable ensemble Gaussian mixture filter. We then showcase that the EnEMF has a significant reduction in error per particle on the 40 -variable Lorenz ‘ 96 system. We answer the titular question, “are non-Gaussian kernels suitable for ensemble mixture model filtering?” in the affirmative.