Density estimation with distribution element trees

@article{Meyer2018DensityEW,
  title={Density estimation with distribution element trees},
  author={Daniel W. Meyer},
  journal={Statistics and Computing},
  year={2018},
  volume={28},
  pages={609-632}
}
  • D. Meyer
  • Published 2 October 2016
  • Computer Science
  • Statistics and Computing
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large… 
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References

SHOWING 1-10 OF 63 REFERENCES
Density Estimation Trees
TLDR
This work states that density estimation in high dimensions remains a challenging problem due to the curse of dimensionality, which affects the convergence rates of many popular density estimation techniques.
Polynomial Histograms for Multivariate Density and Mode Estimation
TLDR
First‐ and second‐order polynomial histogram estimators for a general d‐dimensional setting are presented and pointwise bias and variance of these estimators, their asymptotic mean integrated square error (AMISE), and optimal binwidth are included.
Nonparametric multivariate density estimation using mixtures
TLDR
A new method is proposed for nonparametric multivariate density estimation, which extends a general framework that has been recently developed in the univariate case based onNonparametric and semiparametric mixture distributions, and performs remarkably better than kernel-based density estimators.
EXACT MEAN INTEGRATED SQUARED ERROR
An exact and easily computable expression for the mean integrated squared error (MISE) for the kernel estimator of a general normal mixture density, is given for Gaussian kernels of arbitrary order.
A study of logspline density estimation
Density Estimation in Infinite Dimensional Exponential Families
TLDR
The main goal of the paper is to estimate an unknown density, $p_0$ through an element in $\mathcal{P}$, which involves solving a simple finite-dimensional linear system and it is demonstrated that the proposed estimator outperforms the non-parametric kernel density estimator and grows as $d$ increases.
Coupling Optional Pólya Trees and the Two Sample Problem
TLDR
This work proposes a theoretical framework for inference that addresses challenges in the form of a prior for Bayesian nonparametric analysis based on a random-partition-and-assignment procedure similar to the one that defines the standard optional Pólya tree distribution, but has the ability to generate multiple random distributions jointly.
Functional data analysis for density functions by transformation to a Hilbert space
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints,
...
...