Active set algorithms for estimating shape-constrained density ratios

Dümbgen, Lutz; Mösching, Alexandre; Strähl, Christof (2021). Active set algorithms for estimating shape-constrained density ratios. Computational statistics & data analysis, 163, p. 107300. Elsevier 10.1016/j.csda.2021.107300

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In many instances, imposing a constraint on the shape of a density is a reasonable and flexible assumption. It offers an alternative to parametric models, which can be too rigid, and to other nonparametric methods, which require the choice of tuning parameters. The nonparametric estimation of log-concave or log-convex density ratios is treated by means of active set algorithms in a unified framework. In the setting of log-concave densities, the new algorithm is similar to, but substantially faster than, previously considered active set methods. Log-convexity, on the other hand, is a less common shape-constraint, described by some authors as “tail inflation”. The active set method proposed here is novel in this context. As a by-product, new goodness-of-fit tests of single hypotheses are formulated and are shown to be more powerful than higher criticism tests in a simulation study.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Dümbgen, Lutz and Strähl, Christof

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

0167-9473

Publisher:

Elsevier

Funders:

[4] Swiss National Science Foundation

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

21 Jun 2021 14:35

Last Modified:

27 Jun 2021 03:07

Publisher DOI:

10.1016/j.csda.2021.107300

BORIS DOI:

10.48350/156874

URI:

https://boris.unibe.ch/id/eprint/156874

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