University of Oulu

Holmström, L., Karttunen, K., Klemelä, J. (2017) Estimation of level set trees using adaptive partitions. Computational Statistics, 32 (3), 1139-1163. doi:10.1007/s00180-016-0702-2

Estimation of level set trees using adaptive partitions

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Author: Holmström, Lasse1; Karttunen, Kyösti2; Klemelä, Jussi3
Organizations: 1Department of Mathematical Sciences, University of Oulu, Oulu, Finland
2CEMIS Oulu, University of Oulu, Oulu, Finland
3Helsinki, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 2.1 MB)
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Language: English
Published: Springer Nature, 2017
Publish Date: 2017-12-02


We present methods for the estimation of level sets, a level set tree, and a volume function of a multivariate density function. The methods are such that the computation is feasible and estimation is statistically efficient in moderate dimensional cases (d≈8) and for moderate sample sizes (n≈ 50,000). We apply kernel estimation together with an adaptive partition of the sample space. We illustrate how level set trees can be applied in cluster analysis and in flow cytometry.

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Series: Computational statistics
ISSN: 0943-4062
ISSN-E: 1613-9658
ISSN-L: 0943-4062
Volume: 32
Issue: 3
Pages: 1139 - 1163
DOI: 10.1007/s00180-016-0702-2
Type of Publication: A1 Journal article – refereed
Field of Science: 112 Statistics and probability
Funding: The authors gratefully acknowledge the TEKES funding under project 24301335.
Dataset Reference: The online version of this article (doi:10.1007/s00180-016-0702-2) contains supplementary material, which is available to authorized users.
Copyright information: © Springer-Verlag Berlin Heidelberg 2016. The final publication is available at Springer via