Nonparametric Density Estimation by B-spline Duality

39 Pages Posted: 8 Apr 2019

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Duy Nguyen

Marist College - Department of Mathematics

Date Written: March 11, 2019

Abstract

In this paper, we propose a new non-parametric 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.

Keywords: nonparametric density estimation, spline, empirical characteristic function, empirical density, fast Fourier transform, Levy processes, basis, PROJ, kernel density estimator

JEL Classification: C14, G13, G17, C58, C53, C01

Suggested Citation

Cui, Zhenyu and Kirkby, Justin and Nguyen, Duy, Nonparametric Density Estimation by B-spline Duality (March 11, 2019). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=3352622 or http://dx.doi.org/10.2139/ssrn.3352622

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

Duy Nguyen

Marist College - Department of Mathematics ( email )

NY
United States

HOME PAGE: http://sites.google.com/site/nducduy/

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