Real-Time Density and Mode Estimation With Application to Time-Dynamic Mode Tracking
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Hall, Peter; Muller, Hans-Georg; Wu, Ping-Shi
Description
We introduce a nonparametric time-dynamic kernel type density estimate for the situation where an underlying multivariate distribution evolves with time. Based on this timedynamic density estimate, we propose nonparametric estimates for the time-dynamic mode of the underlying distribution. Our estimators involve boundary kernels for the time dimension so that the estimator is always centered at current time, and multivariate kernels for the spatial dimension of the time-evolving distribution....[Show more]
dc.contributor.author | Hall, Peter | |
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dc.contributor.author | Muller, Hans-Georg | |
dc.contributor.author | Wu, Ping-Shi | |
dc.date.accessioned | 2015-12-07T22:19:31Z | |
dc.identifier.issn | 1061-8600 | |
dc.identifier.uri | http://hdl.handle.net/1885/19386 | |
dc.description.abstract | We introduce a nonparametric time-dynamic kernel type density estimate for the situation where an underlying multivariate distribution evolves with time. Based on this timedynamic density estimate, we propose nonparametric estimates for the time-dynamic mode of the underlying distribution. Our estimators involve boundary kernels for the time dimension so that the estimator is always centered at current time, and multivariate kernels for the spatial dimension of the time-evolving distribution. Under certain mild conditions, the asymptotic behavior of density and mode estimators, especially their uniform convergence in both time and space, is derived. A time-dynamic algorithm for mode tracking is proposed, including automatic bandwidth choices, and is implemented via a mean update algorithm. Simulation studies and real data illustrations demonstrate that the proposed methods work well in practice. | |
dc.publisher | American Statistical Association | |
dc.source | Journal of Computational and Graphical Statistics | |
dc.subject | Keywords: Boundary kernel; Mean-shift algorithm; Modal evolution; Nonparametric estimation; Spatio-temporal modeling; Uniform convergence | |
dc.title | Real-Time Density and Mode Estimation With Application to Time-Dynamic Mode Tracking | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 15 | |
dc.date.issued | 2006 | |
local.identifier.absfor | 010404 - Probability Theory | |
local.identifier.ariespublication | u3488905xPUB8 | |
local.type.status | Published Version | |
local.contributor.affiliation | Hall, Peter, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Muller, Hans-Georg, University of California | |
local.contributor.affiliation | Wu, Ping-Shi, Lehigh University | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 1 | |
local.bibliographicCitation.startpage | 82 | |
local.bibliographicCitation.lastpage | 100 | |
local.identifier.doi | 10.1198/106186006X94333 | |
dc.date.updated | 2015-12-07T08:37:07Z | |
local.identifier.scopusID | 2-s2.0-33645579736 | |
Collections | ANU Research Publications |
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