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SUMMARY:Regression estimation via best L_2-approximation on spaces of step
functions with two jumps
DTSTART;VALUE=DATE-TIME:20220804T070000Z
DTEND;VALUE=DATE-TIME:20220804T072000Z
DTSTAMP;VALUE=DATE-TIME:20240914T202830Z
UID:indico-contribution-1224@conference2.aau.at
DESCRIPTION:In general regression models the equation $Y = m(X) + \\epsilo
n$ holds\, where $X\,Y$ and $\\epsilon$ are random variables\, $m(X) = \\m
athbb{E}[Y \\vert X]$ and the regression function $m$ is unknown.\nThe app
roach by Nadine Albrecht\, 2020\, uses step functions with one jump\, e.g.
binary decision trees\, as an approximation of $m$ in $L_2$ and assumes t
he unique existence of optimal step function parameters for the approximat
ion. With given independent\, identically distributed samples $(X_i\,Y_i)_
{i \\in \\mathbb{N}}$ it is possible to formulate the empirical equivalent
of the approximation via step functions. As a consequence stochastic proc
esses appear in the multivariate Skorokhod space $D(\\mathbb{R}^d)$. \nOur
research interest is the extension to multiple step functions with arbitr
ary\, finite jumps. Under certain conditions first results\, similarly to
the case with one jump\, are examined for step functions with two jumps\,
including stochastic boundedness\, convergence in distribution of the empi
rical processes and consistency of the estimators. By the usage of the Arg
inf theorems introduced by Dietmar Ferger\, 2015\, confidence regions for
the parameters in the step functions can be constructed.\n\nhttps://confer
ence2.aau.at/event/131/contributions/1224/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1224/
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