A least squares-type density estimator using a polynomial function

Jongho Im, Kosuke Morikawa and Hyung-Tae Ha

Computational Statistics & Data Analysis, 2020, vol. 144, issue C

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.

Keywords: Asymptotic distribution; Density estimation; Orthogonal polynomials; Series expansion; Quadratic programming (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302373

DOI: 10.1016/j.csda.2019.106882

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