TheL1theory of estimation of monotone and unimodal densities
- 1 January 1995
- journal article
- research article
- Published by Informa UK Limited in Journal of Nonparametric Statistics
- Vol. 4 (3), 249-261
- https://doi.org/10.1080/10485259508832616
Abstract
This paper investigates the L1-norm of the MLE of monotone and unimodal densities.In the monotonecase, it is shown that converges in distribution to the sum of anormal r.v and the maxima of a Brownian bridge over the flat ranges of the monotone density. In the unimodal case, itis shown that, if an -consistent mode estimate is used to construct the plug-in MLE of the unimodal density with unknown mode, the L1-norm of the plug-in MLE is equal to that of the MLE of theunimoral density with known mode up to the order . Therefore, the limiting distributions of the L1-norms of these two estimates are the same.Keywords
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