Minimax Density Estimation for Growing Dimension

Daniel McDonald
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:194-203, 2017.

Abstract

This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which gives the worst-case rate over standard classes of smooth densities, and we show that kernel density estimators achieve this rate. We also give oracle choices for the bandwidth and derive the fastest rate $d$ can grow with $n$ to maintain estimation consistency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-mcdonald17a, title = {{Minimax Density Estimation for Growing Dimension}}, author = {McDonald, Daniel}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {194--203}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/mcdonald17a/mcdonald17a.pdf}, url = {https://proceedings.mlr.press/v54/mcdonald17a.html}, abstract = {This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which gives the worst-case rate over standard classes of smooth densities, and we show that kernel density estimators achieve this rate. We also give oracle choices for the bandwidth and derive the fastest rate $d$ can grow with $n$ to maintain estimation consistency.} }
Endnote
%0 Conference Paper %T Minimax Density Estimation for Growing Dimension %A Daniel McDonald %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-mcdonald17a %I PMLR %P 194--203 %U https://proceedings.mlr.press/v54/mcdonald17a.html %V 54 %X This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which gives the worst-case rate over standard classes of smooth densities, and we show that kernel density estimators achieve this rate. We also give oracle choices for the bandwidth and derive the fastest rate $d$ can grow with $n$ to maintain estimation consistency.
APA
McDonald, D.. (2017). Minimax Density Estimation for Growing Dimension. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:194-203 Available from https://proceedings.mlr.press/v54/mcdonald17a.html.

Related Material