B-Spline Density Estimation Library

Supports nonparametric density estimation using B-Spline density estimator from univariate sample.

Estimation methods supported:

• Empirical Characteristic Function (ECF): Cui, Kirkby and Nguyen (2019)
• Galerkin Method: Kirkby, Leitao and Nguyen, (2021)
• "Primal" Basis Estimation: Redner (1999)

Bandwidth Selection methods supported:

• LCV - Likelihood Cross-Validation
• LSCV - Least-Squares Cross-Validation
• Apdaptive Rule of Thumb - Adaptive heuristic rule of thumb, See Cui, Kirkby and Nguyen (2019)
• Plugin - uses plugin method based on estimate of roughness
• Normal Rule - traditional normal rule of thumb

Acknowledgement: These libraries have been built in collaboration with:

• Justin Lars Kirkby
• Alvaro Leitao-Rodriguez
• Duy Nguyen
• Zhenyu Cui

Supporting Research Articles:

• Nonparametric Density Estimation by B-spline Duality. Econometric Theory (2019)
• Nonparametric Density Estimation and Bandwidth Selection with B-spline bases: a Novel Galerkin Method. Computational Statistics and Data Analysis (2021)
• A data-driven framework for consistent financial valuation and risk measurement. Eur. J. Operational Research (2020)