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info.json
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{
"abstract": "We consider so-called univariate unlinked (sometimes ``decoupled,'' or ``shuffled'') regression when the unknown regression curve is monotone. In standard monotone regression, one observes a pair $(X,Y)$ where a response $Y$ is linked to a covariate $X$ through the model $Y= m_0(X) + \\epsilon$, with $m_0$ the (unknown) monotone regression function and $\\epsilon$ the unobserved error (assumed to be independent of $X$). In the unlinked regression setting one gets only to observe a vector of realizations from both the response $Y$ and from the covariate $X$ where now $Y \\stackrel{d}{=} m_0(X) + \\epsilon$. There is no (observed) pairing of $X$ and $Y$. Despite this, it is actually still possible to derive a consistent non-parametric estimator of $m_0$ under the assumption of monotonicity of $m_0$ and knowledge of the distribution of the noise $\\epsilon$. In this paper, we establish an upper bound on the rate of convergence of such an estimator under minimal assumption on the distribution of the covariate $X$. We discuss extensions to the case in which the distribution of the noise is unknown. We develop a second order algorithm for its computation, and we demonstrate its use on synthetic data. Finally, we apply our method (in a fully data driven way, without knowledge of the error distribution) on longitudinal data from the US Consumer Expenditure Survey.",
"authors": [
"Fadoua Balabdaoui",
"Charles R. Doss",
"C\u00e9cile Durot"
],
"emails": [
"fadoua.balabdaoui@stat.math.ethz.ch",
"cdoss@umn.edu",
"cecile.durot@gmail.com"
],
"id": "20-689",
"issue": 172,
"pages": [
1,
60
],
"title": "Unlinked Monotone Regression",
"volume": 22,
"year": 2021
}