Deconvolving Multivariate Density from Random Field |
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Authors: | Yuan Ming |
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Institution: | (1) Department of Statistics, University of Wisconsin, 1210 West Dayton Street, Madison, WI, 53706, U.S.A. |
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Abstract: | We consider the problem of estimating a continuous bounded multivariate probability density function (pdf) when the random
field X
i
, i ∈ Z
d
from the density is contaminated by measurement errors. In particular, the observations Y
i
, i ∈ Z
d
are such that Y
i
= X
i
+ ε
i
, where the errors ε
i
are a sample from a known distribution. We improve the existing results in at least two directions. First, we consider random
vectors in contrast to most existing results which are only concerned with univariate random variables. Secondly, and most
importantly, while all the existing results focus on the temporal cases (d = 1), we develop the results for random vectors with a certain spatial interaction. Precise asymptotic expressions and bounds
on the mean-squared error are established, along with rates of both weak and strong consistencies, for random fields satisfying
a variety of mixing conditions. The dependence of the convergence rates on the density of the noise field is also studied.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | strong mixing kernel density estimation deconvolution mean squared error strong consistency random field |
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