Density estimation on a network

Yang Liu and David Ruppert

Computational Statistics & Data Analysis, 2021, vol. 156, issue C

Abstract: A novel approach is proposed for density estimation on a network. Nonparametric density estimation on a network is formulated as a nonparametric regression problem by binning. Nonparametric regression using local polynomial kernel-weighted least squares have been studied rigorously, and its asymptotic properties make it superior to kernel estimators such as the Nadaraya–Watson estimator. When applied to a network, the best estimator near a vertex depends on the amount of smoothness at the vertex. Often, there are no compelling reasons to assume that a density will be continuous or discontinuous at a vertex, hence a data driven approach is proposed. To estimate the density in a neighborhood of a vertex, a two-step procedure is proposed. The first step of this pretest estimator fits a separate local polynomial regression on each edge using data only on that edge, and then tests for equality of the estimates at the vertex. If the null hypothesis is not rejected, then the second step re-estimates the regression function in a small neighborhood of the vertex, subject to a joint equality constraint. Since the derivative of the density may be discontinuous at the vertex, a piecewise polynomial local regression estimate is used to model the change in slope. The special case of local piecewise linear regression is studied in detail and the leading bias and variance terms are derived using weighted least squares theory. The proposed approach will remove the bias near a vertex that has been noted for existing methods, which typically do not allow for discontinuity at vertices. For a fixed network, the proposed method scales sub-linearly with sample size and it can be extended to regression and varying coefficient models on a network. The working of the proposed model is demonstrated by simulation studies and applications to a dendrite network dataset.

Keywords: Asymptotic bias and variance; Discontinuous density; Kernel density estimation; Local piecewise linear estimation; Pretest estimation (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016794732030219X
Full text for ScienceDirect subscribers only.

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:eee:csdana:v:156:y:2021:i:c:s016794732030219x

DOI: 10.1016/j.csda.2020.107128

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().