Minimum local distance density estimation
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1412.2851.pdf
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Author(s)
Tenorio, Luis
Garg, Vikram V
Willcox, Karen E
Date Issued
February 2016
Journal
Communications in Statistics - Theory and Methods
Publisher
Informa UK Limited
Citation
Garg, Vikram V., et al. “Minimum Local Distance Density Estimation.” Communications in Statistics - Theory and Methods, vol. 46, no. 1, Jan. 2017, pp. 148–64. © 2017 Taylor & Francis Group, LLC
Version
Original manuscript
Abstract
We present a local density estimator based on first-order statistics. To estimate the density at a point, x, the original sample is divided into subsets and the average minimum sample distance to x over all such subsets is used to define the density estimate at x. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/03610926.2014.988260
