Density estimation of a sum random variable from contaminated data samples
Let X, Y be independent random variables with unknown distributions and f X + Y be the unknown density of X + Y. Under the effects of independent random noises ζ and η, which are assumed to have known distributions, we observe the random variables X ′ and Y ′ , where X ′ = X + ζ and Y ′ = Y + η . Ou...
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Published in | Communications in statistics. Simulation and computation Vol. 53; no. 6; pp. 2822 - 2841 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Taylor & Francis
02.06.2024
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | Let X, Y be independent random variables with unknown distributions and
f
X
+
Y
be the unknown density of X + Y. Under the effects of independent random noises ζ and η, which are assumed to have known distributions, we observe the random variables
X
′
and
Y
′
,
where
X
′
=
X
+
ζ
and
Y
′
=
Y
+
η
.
Our aim is to estimate nonparametrically
f
X
+
Y
on the basis of random samples from the distributions of
X
′
,
Y
′
.
Using the observed data, we suggest an estimator of
f
X
+
Y
and show that it is consistent with respect to the mean integrated squared error. Under some conditions restricted to the smoothness of the noises as well as of the variable X + Y, we derive some upper and lower bounds on the convergence rate of the error. We also conduct some simulations to illustrate the efficient of our method. |
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ISSN: | 0361-0918 1532-4141 |
DOI: | 10.1080/03610918.2022.2091780 |