 Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptionsEva Herrmann and Klaus Ziegler Statistics & Probability Letters, 2004, vol. 68, issue 4, 359-368 Abstract: Nonparametric estimation of the mode of a density or regression function via kernel methods is considered. It is shown that the rate of consistency of the mode estimator can be determined without the typical smoothness conditions. Only the uniform rate of the so-called stochastic part of the problem together with some mild conditions characterizing the shape or "acuteness" of the mode influence the rate of the mode estimator. In particular, outside the location of the mode, our assumptions do not even imply continuity. Overall, it turns out that the location of the mode can be estimated at a rate that is the better the "peakier" (and hence nonsmooth) the mode is, while the contrary holds with estimation of the size of the mode. Keywords: Nonparametric; curve; estimation; Mode; Kernel; smoothing; Rates; of; consistency; Nonsmooth; curves (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:68:y:2004:i:4:p:359-368 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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