Confidence bands for convex median curves using sign-tests
| dc.creator | Duembgen, Lutz | |
| dc.date | 2006-09-11 | |
| dc.date | 2007-09-06 | |
| dc.date.accessioned | 2026-07-07T09:23:38Z | |
| dc.date.available | 2026-07-07T09:23:38Z | |
| dc.description | Suppose 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.description | Published 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.identifier | https://arxiv.org/abs/math/0609285 | |
| dc.identifier | http://arxiv.org/abs/math/0609285 | |
| dc.identifier | IMS Lecture Notes Monograph Series 2007, Vol. 55, 85-100 | |
| dc.identifier | doi:10.1214/074921707000000283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155801 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G08, 62G15, 62G20 (Primary) 62G35 (Secondary) | |
| dc.title | Confidence bands for convex median curves using sign-tests | |
| dc.type | text |