JonasMoss
commented
6 years ago I'm not optimistic this is possible. The FFT method is based on convolutions, which 1.) our parametric starts destroy, 2.) are incompatible with asymmetric kernels. The approach of Raykar might work but would take a massive load of time to deduce.
Our main competitors are:
Currently we are unable to compete with these in terms of computing speed. This is because they use a combination of data binning and FFT (fast Fourier transform) in order to compute the estimates. The difference in computation speed is likely to be huge when we move to larger dimensions. Thus I suggest we implement data binning / FFT as an option (standard option).
The main source on FFT binning is Wand's 1994 paper. Never papers include "FFT-Based Fast Computation of Multivariate Kernel Density Estimators with Unconstrained Bandwidth Matrices" and "FFT-Based Fast Bandwidth Selector for Multivariate Kernel Density Estimation", both by Gramacki and Gramacki.
Another promising one is Raykar et al's paper from 2012. They claim to outperform binning both in terms of accuracy and speed. It might be complicated though.
I might add that it would be interesting in itself to extend the method to parametric starts, maybe worth a paper. In addition, I think asymmetric kernels and data transformation methods haven't been studied in this context yet.
Subsequently, we should run a simulation study to compare the speed of all the methods. This will show our method is comparable.