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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 46, Fasc. 1,
pages 87 - 103
DOI: 10.37190/0208-4147.00305
Published online 5.10.2026
 

On the uniformly complete consistency of density estimation via frequency polygons under ρ-mixing random fields

X. Deng
Y. Ding
Y. Wang
M. Ge

Abstract:

The convergence properties of a density estimator constructed from frequency polygons are investigated under the condition that the samples are drawn from a ρ-mixing random field. Using the properties and the moment inequalities for ρ-mixing random fields, the uniformly complete consistency is established for density estimation via frequency polygons for such random fields, and the corresponding convergence rate is derived. The results obtained further improve and extend the relevant research findings of Carbon (2007) and Wang et al. (2021).

2010 AMS Mathematics Subject Classification: Primary 60G05; Secondary 62G20.

Keywords and phrases: ρ-mixing random field, frequency polygon, complete consistency, convergence rate.

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