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SUMMARY:Multiplicative deconvolution under unknown error distribution
DTSTART;VALUE=DATE-TIME:20220804T140000Z
DTEND;VALUE=DATE-TIME:20220804T142000Z
DTSTAMP;VALUE=DATE-TIME:20240618T021015Z
UID:indico-contribution-201-1217@conference2.aau.at
DESCRIPTION:In this talk\, we construct a nonparametric estimator of the d
ensity $f:\\mathbb R_+ \\rightarrow \\mathbb R_+$ of a positive random var
iable $X$ based on an i.i.d. sample $(Y_1\, \\dots\, Y_n)$ of\n\\begin{equ
ation}Y=X\\cdot U\,\n\\end{equation} where $U$ is a second positive random
variable independent of $X$. More precisely\, we consider the case where
the distribution of $U$ is unknown but an i.i.d. sample $(\\widetilde U_1\
, \\dots\, \\widetilde U_m)$ of the error random variable $U$ is given. \n
Based on the estimation of the Mellin transforms of $Y$ and $U$\, and a sp
ectral cut-off regularisation of the inverse Mellin transform\, we propose
a fully data-driven density estimator where the choice of the spectral cu
t-off parameter is dealt by a model selection approach. We demonstrate the
reasonable performance of our estimator using a Monte-Carlo simulation.\n
\nhttps://conference2.aau.at/event/131/contributions/1217/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1217/
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SUMMARY:Measuring statistical dependency with optimal transport
DTSTART;VALUE=DATE-TIME:20220804T133000Z
DTEND;VALUE=DATE-TIME:20220804T135000Z
DTSTAMP;VALUE=DATE-TIME:20240618T021015Z
UID:indico-contribution-201-1222@conference2.aau.at
DESCRIPTION:In this talk\, we introduce a novel framework for measuring st
atistical dependency between two random variables $X$ and $Y$\, the *trans
port dependency* $\\tau(X\, Y) \\ge 0$. This coefficient relies on the not
ion of optimal transport and is applicable to random variables\, taking va
lues in general Polish spaces. It can be estimated consistently via the co
rresponding empirical measure\, is versatile and adaptable to various scen
arios by proper choices of the cost function\, and intrinsically respects
metric properties of the ground spaces. Notably\, statistical independence
is characterized by $\\tau(X\, Y) = 0$\, while large values of $\\tau(X\,
Y)$ indicate highly regular relations between $X$ and $Y$. Indeed\, for s
uitable base costs\, $\\tau(X\, Y)$ is maximized if and only if $Y$ can be
expressed as 1-Lipschitz function of $X$ or vice versa.\nWe exploit this
characterization and define a class of dependency coefficients with values
in $[0\, 1]$\, which can emphasizes different functional relations. In p
articular\, for suitable costs the *transport correlations* is symmetric a
nd attains the value $1$ if and only if $Y = f(X)$ where $f$ is a multiple
of an isometry\, which makes it comparable to the distance correlation.\n
Finally we illustrate how the transport dependency can be used in practice
to explore dependencies between random variables\, in a gene expression s
tudy.\n\nhttps://conference2.aau.at/event/131/contributions/1222/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1222/
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