Adaptive Nonparametric Density Estimation with B-Spline Bases

Yanchun Zhao, Mengzhu Zhang, Qian Ni and Xuhui Wang ()
Additional contact information
Yanchun Zhao: School of Mathematics, Hefei University of Technology, Hefei 230009, China
Mengzhu Zhang: School of Mathematics, Hefei University of Technology, Hefei 230009, China
Qian Ni: School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China
Xuhui Wang: Department of Mathematics, Hohai University, Nanjing 211100, China

Mathematics, 2023, vol. 11, issue 2, 1-12

Abstract: Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can improve on the approximation capability of uniform B-splines. Based on this observation, we perform density estimation with nonuniform B-splines. By introducing the error indicator attached to each interval, we propose an adaptive strategy to generate the nonuniform knot vector. The error indicator is an approximation of the information entropy locally, which is closely related to the number of kernels when we construct the nonuniform estimator. The numerical experiments show that, compared with the uniform B-spline, the local density estimation with nonuniform B-splines not only achieves better estimation results but also effectively alleviates the overfitting phenomenon caused by the uniform B-splines. The comparison with the existing estimation procedures, including the state-of-the-art kernel estimators, demonstrates the accuracy of our new method.

Keywords: adaptive strategy; B-spline; nonparametric density estimation; error indictor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/2/291/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/2/291/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:2:p:291-:d:1026745

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().