Confidence bands for convex median curves using sign-tests

dc.creatorDuembgen, Lutz
dc.date2006-09-11
dc.date2007-09-06
dc.date.accessioned2026-07-07T09:23:38Z
dc.date.available2026-07-07T09:23:38Z
dc.descriptionSuppose that one observes pairs $(x_1,Y_1)$, $(x_2,Y_2)$, ..., $(x_n,Y_n)$, where $x_1\le x_2\le ... \le x_n$ are fixed numbers, and $Y_1,Y_2,...,Y_n$ are independent random variables with unknown distributions. The only assumption is that ${\rm Median}(Y_i)=f(x_i)$ for some unknown convex function $f$. We present a confidence band for this regression function $f$ using suitable multiscale sign-tests. While the exact computation of this band requires $O(n^4)$ steps, good approximations can be obtained in $O(n^2)$ steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size $n$ tends to infinity.
dc.descriptionPublished at http://dx.doi.org/10.1214/074921707000000283 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0609285
dc.identifierhttp://arxiv.org/abs/math/0609285
dc.identifierIMS Lecture Notes Monograph Series 2007, Vol. 55, 85-100
dc.identifierdoi:10.1214/074921707000000283
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155801
dc.subjectStatistics Theory
dc.subject62G08, 62G15, 62G20 (Primary) 62G35 (Secondary)
dc.titleConfidence bands for convex median curves using sign-tests
dc.typetext

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