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NONPARAMETRIC DENSITY ESTIMATION BY B-SPLINE DUALITY

Published online by Cambridge University Press:  23 May 2019

Zhenyu Cui ,
Justin Lars Kirkby  and
Duy Nguyen
Zhenyu Cui
Affiliation:
Stevens Institute of Technology
Justin Lars Kirkby*
Affiliation:
Georgia Institute of Technology
Duy Nguyen
Affiliation:
Marist College
*
*Address correspondence to J. Lars Kirkby, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30318, USA; e-mail: jkirkby3@gatech.edu.
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Abstract

In this article, we propose a new nonparametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density estimator based on the class of B-splines and derive its theoretical properties, including the asymptotically optimal choice of bandwidth. Detailed theoretical analysis and comparisons of our estimator with existing local basis and kernel density estimators are presented. The estimator is particularly well suited for high-frequency data analysis in financial and economic markets.

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ARTICLES
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Econometric Theory , Volume 36 , Issue 2 , April 2020 , pp. 250 - 291
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Copyright © Cambridge University Press 2019 

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