A least squares-type density estimator using a polynomial function

Jongho Im, Kosuke Morikawa, Hyung Tae Ha

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1 Citation (Scopus)


Higher-order density approximation and estimation methods using orthogonal series expansion have been extensively discussed in statistical literature and its various fields of application. This study proposes least squares-type estimation for series expansion via minimizing the weighted square difference of series distribution expansion and a benchmarking distribution estimator. As the least squares-type estimator has an explicit expression, similar to the classical moment-matching technique, its asymptotic properties are easily obtained under certain regularity conditions. In addition, we resolve the non-negativity issue of the series expansion using quadratic programming. Numerical examples with various simulated and real datasets demonstrate the superiority of the proposed estimator.

Original languageEnglish
Article number106882
JournalComputational Statistics and Data Analysis
Publication statusPublished - 2020 Apr

Bibliographical note

Funding Information:
We thank the Editor, the Associate Editor and two anonymous reviewers for their constructive comments and suggestions, which have significantly improved the overall quality of our paper. The research of the first author was supported by the Yonsei University Research Fund2018-22-0043. The second author was supported by JSPS KAKENHI (19K14592), and the third author by National Research Foundation of Korea (2017R1E1A1A03070290).

Publisher Copyright:
© 2019 Elsevier B.V.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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