Polynomial Histograms for Multivariate Density and Mode Estimation
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Jing, Junmei; Koch, Inge; Naito, Kanta
Description
We consider the problem of efficiently estimating multivariate densities and their modes for moderate dimensions and an abundance of data. We propose polynomial histograms to solve this estimation problem. We present first- and second-order polynomial histogram estimators for a general d-dimensional setting. Our theoretical results include pointwise bias and variance of these estimators, their asymptotic mean integrated square error (AMISE), and optimal binwidth. The asymptotic performance of...[Show more]
dc.contributor.author | Jing, Junmei | |
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dc.contributor.author | Koch, Inge | |
dc.contributor.author | Naito, Kanta | |
dc.date.accessioned | 2015-12-10T22:59:35Z | |
dc.identifier.issn | 0303-6898 | |
dc.identifier.uri | http://hdl.handle.net/1885/61156 | |
dc.description.abstract | We consider the problem of efficiently estimating multivariate densities and their modes for moderate dimensions and an abundance of data. We propose polynomial histograms to solve this estimation problem. We present first- and second-order polynomial histogram estimators for a general d-dimensional setting. Our theoretical results include pointwise bias and variance of these estimators, their asymptotic mean integrated square error (AMISE), and optimal binwidth. The asymptotic performance of the first-order estimator matches that of the kernel density estimator, while the second order has the faster rate of O(n-6/(d+6)). For a bivariate normal setting, we present explicit expressions for the AMISE constants which show the much larger binwidths of the second order estimator and hence also more efficient computations of multivariate densities. We apply polynomial histogram estimators to real data from biotechnology and find the number and location of modes in such data. | |
dc.publisher | Wiley-Blackwell | |
dc.source | Scandinavian Journal of Statistics | |
dc.subject | Keywords: Asymptotic performance; Estimation of modes; Multivariate density estimation; Polynomial histogram estimators | |
dc.title | Polynomial Histograms for Multivariate Density and Mode Estimation | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 39 | |
dc.date.issued | 2012 | |
local.identifier.absfor | 010405 - Statistical Theory | |
local.identifier.ariespublication | f5625xPUB591 | |
local.type.status | Published Version | |
local.contributor.affiliation | Jing, Junmei, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Koch, Inge, University of Adelaide | |
local.contributor.affiliation | Naito, Kanta, Shimane University | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 1 | |
local.bibliographicCitation.startpage | 75 | |
local.bibliographicCitation.lastpage | 96 | |
local.identifier.doi | 10.1111/j.1467-9469.2011.00764.x | |
dc.date.updated | 2016-02-24T09:27:25Z | |
local.identifier.scopusID | 2-s2.0-84857035947 | |
local.identifier.thomsonID | 000309598700002 | |
Collections | ANU Research Publications |
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