Researchers have proposed density estimation via mixture discrepancy and moments as alternative methods to the star discrepancy for generalizing histogram statistics to higher dimensional cases.
The density estimation via mixture discrepancy based sequential partition (DSP-mix) and density estimation via moments based sequential partition (MSP) are computationally tractable and exhibit reflection and rotation invariance.
Both DSP-mix and MSP run approximately ten times faster than density estimation via discrepancy based sequential partition (DSP) while maintaining the same accuracy.
Numerical experiments demonstrate the efficiency of DSP-mix and MSP in reconstructing the d-D mixture of Gaussians and Betas for various dimensions.