A new method for nonparametric density estimation

Abstract

A new method for computing the probability distribution of a given sample of data is proposed. The observations are mapped into the finite interval [-1,1] and a shape-preserving spline is used to calculate the derivative of the cumulative distribution function. Although based on a spline, the procedure guarantees non-negative density estimates. The method is compared to a normal kernel with plug-in bandwidth for a range of test distributions. As well as requiring less computational effort, the performance of the spline estimate of density is marginally superior to that of the kernel for distributions that have an infinite domain, but is currently inferior to second generation kernels for semi-infinite domains.

Keywords:

• Density estimation
• shape-preserving spline
• mapping functions
• node selection
• normal kernel
• plug-in bandwidth

^*Address for correspondence: School of Economics and Finance, Queensland University of Technology, Gardens Point Campus, 2 George Street, Brisbane Q 4001, Australia, [email protected]

^*Address for correspondence: School of Economics and Finance, Queensland University of Technology, Gardens Point Campus, 2 George Street, Brisbane Q 4001, Australia, [email protected]

Notes

^*Address for correspondence: School of Economics and Finance, Queensland University of Technology, Gardens Point Campus, 2 George Street, Brisbane Q 4001, Australia, [email protected]