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Nonparametric Density Estimation By B-Spline Duality

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  • Cui, Zhenyu
  • Kirkby, Justin Lars
  • Nguyen, Duy

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.

Suggested Citation

  • Cui, Zhenyu & Kirkby, Justin Lars & Nguyen, Duy, 2020. "Nonparametric Density Estimation By B-Spline Duality," Econometric Theory, Cambridge University Press, vol. 36(2), pages 250-291, April.
    • Handle: RePEc:cup:etheor:v:36:y:2020:i:2:p:250-291_3
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    Cited by:

    1. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "A data-driven framework for consistent financial valuation and risk measurement," European Journal of Operational Research, Elsevier, vol. 289(1), pages 381-398.
    2. R. H. Ilyasov & V. A. Plotnikov, 2022. "Oil Production and Carbon Emissions: Spline Analysis of Relationships," Administrative Consulting, Russian Presidential Academy of National Economy and Public Administration. North-West Institute of Management., issue 5.
    3. Yanchun Zhao & Mengzhu Zhang & Qian Ni & Xuhui Wang, 2023. "Adaptive Nonparametric Density Estimation with B-Spline Bases," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    4. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    5. Wang, Yayun & Zhang, Zhimin & Yu, Wenguang, 2021. "Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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