The locally Gaussian density estimator for multivariate data

The locally Gaussian density estimator for multivariate data It is well known that the Curse of Dimensionality causes the standard Kernel Density Estimator to break down quickly as the number of variables increases. In non-parametric regression, this effect is relieved in various ways, for example by assuming additivity or some other simplifying structure on the interaction between variables. This paper presents the Locally Gaussian Density Estimator (LGDE), which introduces a similar idea to the problem of density estimation. The LGDE is a new method for the non-parametric estimation of multivariate probability density functions. It is based on preliminary transformations of the marginal observation vectors towards standard normality, and a simplified local likelihood fit of the resulting distribution with standard normal marginals. The LGDE is introduced, and asymptotic theory is derived. In particular, it is shown that the LGDE converges at a speed that does not depend on the dimension. Examples using real and simulated data confirm that the new estimator performs very well on finite sample sizes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistics and Computing Springer Journals

The locally Gaussian density estimator for multivariate data

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Statistics; Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science
ISSN
0960-3174
eISSN
1573-1375
D.O.I.
10.1007/s11222-016-9706-6
Publisher site
See Article on Publisher Site

Abstract

It is well known that the Curse of Dimensionality causes the standard Kernel Density Estimator to break down quickly as the number of variables increases. In non-parametric regression, this effect is relieved in various ways, for example by assuming additivity or some other simplifying structure on the interaction between variables. This paper presents the Locally Gaussian Density Estimator (LGDE), which introduces a similar idea to the problem of density estimation. The LGDE is a new method for the non-parametric estimation of multivariate probability density functions. It is based on preliminary transformations of the marginal observation vectors towards standard normality, and a simplified local likelihood fit of the resulting distribution with standard normal marginals. The LGDE is introduced, and asymptotic theory is derived. In particular, it is shown that the LGDE converges at a speed that does not depend on the dimension. Examples using real and simulated data confirm that the new estimator performs very well on finite sample sizes.

Journal

Statistics and ComputingSpringer Journals

Published: Oct 5, 2016

References

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