Transmetric density estimation is a generalization of kernel density estimation that is proposed in Hovda
(2014) and Hovda (2016), This framework involves the possibility of making assumptions on the kernel of the distribution to improve convergence orders and to reduce the number of dimensions in the graphical display.  In this paper we show that several state-of-the-art nonparametric, semiparametric and even parametric methods are special cases of this formulation, meaning that there is a unified approach.

 

Moreover, it is shown that parameters can be trained using unbiased cross-validation.  When parameter estimation is included, the mean integrated squared error of the transmetric density estimator is lower than for the common kernel density estimator, when the number of dimensions is larger than two.