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Some problems on the estimation of unimodal densities

Peter J Bickel Jianqing Fan

Statistics Theory and Methods mathscidoc:1912.43321

Statistica Sinica, 23-45, 1996.1
In this paper, we study, in some new ways, the estimation of unimodal densities. Several methods for estimating unimodal densities are proposed: plug-in MLE, pregrouping techniques, linear spline MLE. Based on the maximum likelihood method, an automatic procedure for estimating a unimodal density as well as its mode is proposed. We also give asymptotic theory for the proposed estimators. An important consequence of this study is that having to estimate the location of a mode does not affect the limiting behavior of the proposed unimodal density estimate. Simulation studies illustrate the proposed methods.
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@inproceedings{peter1996some,
  title={Some problems on the estimation of unimodal densities},
  author={Peter J Bickel, and Jianqing Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113709827163881},
  booktitle={Statistica Sinica},
  pages={23-45},
  year={1996},
}
Peter J Bickel, and Jianqing Fan. Some problems on the estimation of unimodal densities. 1996. In Statistica Sinica. pp.23-45. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113709827163881.
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