A least squares-type density estimator using a polynomial function

Jongho Im; Kosuke Morikawa; Hyung Tae Ha

doi:10.1016/j.csda.2019.106882

A least squares-type density estimator using a polynomial function

Jongho Im, Kosuke Morikawa, Hyung Tae Ha

Department of Applied Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Article number	106882
Journal	Computational Statistics and Data Analysis
Volume	144
DOIs	https://doi.org/10.1016/j.csda.2019.106882
Publication status	Published - 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

Access to Document

10.1016/j.csda.2019.106882

Cite this

@article{978e3eaf57264e80b3587483dc7d8ced,

title = "A least squares-type density estimator using a polynomial function",

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.",

author = "Jongho Im and Kosuke Morikawa and Ha, {Hyung Tae}",

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: {\textcopyright} 2019 Elsevier B.V.",

year = "2020",

month = apr,

doi = "10.1016/j.csda.2019.106882",

language = "English",

volume = "144",

journal = "Computational Statistics and Data Analysis",

issn = "0167-9473",

publisher = "Elsevier",

}

TY - JOUR

T1 - A least squares-type density estimator using a polynomial function

AU - Im, Jongho

AU - Morikawa, Kosuke

AU - Ha, Hyung Tae

N1 - 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.

PY - 2020/4

Y1 - 2020/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85075831425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075831425&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2019.106882

DO - 10.1016/j.csda.2019.106882

M3 - Article

AN - SCOPUS:85075831425

SN - 0167-9473

VL - 144

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

M1 - 106882

ER -

A least squares-type density estimator using a polynomial function

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this