A least squares-type density estimator using a polynomial function

Jongho Im, Kosuke Morikawa, Hyung Tae Ha

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Abstract

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
Volume144
DOIs
Publication statusPublished - 2020 Apr

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All Science Journal Classification (ASJC) codes

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

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